# GATE CSE 2021 Set 1 | GA Question: 9

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Given below are two statements $1$ and $2$, and two conclusions $\text{I}$ and $\text{II}$

• $\text{Statement 1:}$ All bacteria are microorganisms.
• $\text{Statement 2:}$ All pathogens are microorganisms.
• $\text{Conclusion I:}$ Some pathogens are bacteria.
• $\text{Conclusion II:}$ All pathogens are not bacteria.

Based on the above statements and conclusions, which one of the following options is logically $\text{CORRECT}$?

1. Only conclusion $\text{I}$ is correct
2. Only conclusion $\text{II}$ is correct
3. Either conclusion $\text{I}$ or $\text{II}$ is correct
4. Neither conclusion $\text{I}$ nor $\text{II}$ is correct

recategorized ago
5

WELL FIRST OF ALL

EITHER OR    MEANS A XOR B

NOW 4  CASES

AM CONSIDERING THE CASE WHEN  PATHOGENS AND BACTERIA INTERSECTS  TO PROVE THAT WE CAN’T CONCLUDE  C

NOW CONCLUSIONS

1  SOME PATHOGENS ARE BACTERIA -SATISFIED

2 ALL PATHOGENS ARE NOT BACTERIA -SATISFIED

NOW I WILL PROVE EITHER OR IS WRONG

FOR  C TO BE RIGHT   ( CONCLUSION 1 XOR CONCLUSION  2 ) MUST BE TRUE

I.E (TRUE XOR TRUE )MUST BE TRUE BUT THAT IS NOT THE CASE ...SO  C CAN’T BE THE ANSWER .

…………………………………………………………………………………………………………………

NOW AS WE HAVE PROVED THAT EITHER OF THEM CAN’T BE TRUE (ALWAYS),NOW WE HAVE TO NULLIFY  OPTION 1 AND OPTION 2 WHICH IS QUITE TRIVIAL

IF PATHOGENS AND BACTRIA ARE DISJOINT THEN CONCLUSION 1 IS NOT VALID

IF BACTERIA IS A SUPERSET OF PATHOGEN CONCLUSION 2 IS NOT VALID

--------------------------------------------------------------------------------------------------------------------------------------HENCE ANSWER IS  D

CORRECT ME IF ANYTHING IS WRONG

NOW CONFIRMING MY 2ND CONCLUSION

0
I think its

Either-OR case:

Condition of Either-OR case:

1) both conclusions false.

2) subject and object same in both conclusion.

3) one negative and one positive conclusion.

.…

And

Primary Condition:

Both statements connected some common term:

Here microorganism is common term.

Hence

Option C is correct.

Hope its help u.
0
Someone  plzz challenge this question...
1

I think answer should be D: neither 1 nor 2
EXPLAINATION
Either-OR is similar to XOR gate which means both conclusions can't be true at the same time.
But in the question both conclusions can be true at same time.
So, option D): neither 1 nor 2 is correct seems most logical answer.

NOTE
conclusion 2 means :- Not every Pathogen is Bacteria. which means some pathogens can be bacteria.

Hope You Understand.

But i think marks should be awarded to all as the conclusion 2 could have different meanings.
but still option D is necessarily true.

1
Congratulations Guys. Both answers are correct as per final answer key..

WE WON!!!

$pathogen(x)$ = x is pathogen

$bacteria(x)$ = x is bacteria

Conclusion I: Some pathogens are bacteria.

$\exists x ( pathogen(x) \wedge bacteria(x))$

this means  $pathogen \cap bacteria \neq \phi$

Conclusion II: All pathogens are not bacteria.

$\forall x ( pathogen(x) \rightarrow \sim bacteria(x))$

this means $pathogen \cap bacteria = \phi$

clearly either conclusion I or conclusion is true.

I think confusion here is in second conclusion,

if the given conclusion II were like

“Not all pathogens are bacteria”,     $\sim (\forall x ( pathogen(x) \rightarrow bacteria(x)))$

in the case i agree niether is correct answer..

But see the difference between given conclusion and this conclusion..

Correct me if I’m wrong!

1
$P(x,y)$ : student x marked the answer y

$U(x)$ : x is ready to understand this problem

“All students who marked the answer D are not ready to understand this problem”

$\forall x(\ P(x,D) \rightarrow \sim U(x)\ )$   :p
0
@Nikhil_dhama xDDDDDDDDDDDDDDDDD
0

@debmalyaSEN

You said

”All chefs are not masterchefs”

by this i mean there exist some chef who is not a masterchef

by this we don’t mean  for every person in the universe if it’s a chef then he is not a masterchef .

In the question

• Conclusion I:Conclusion I: Some pathogens are bacteria.
• Conclusion II:Conclusion II: All pathogens are not bacteria

There can be two possible cases

Consider Case 1

Where bacteria and pathogen are both subsets of microorganisms &

Bacteria ∩ Pathogen = null

For this case

Conclusion I fails but conclusion II passes

So we rule out Option A & D

Consider Case 2

Where bacteria and pathogen are both subsets of microorganisms &

Bacteria ∩ Pathogen = not null

For this case

Conclusion I passes but conclusion II fails

So we rule out Option B now

Now the question doesn’t say if its OR or XOR

and only conclusive logic we can derive is XOR

So C satisfies either one of the conditions at a time

It can never satisfy both or none cause its like

Schrödinger's cat experiment

The cat can either be alive or dead

It cannot be both dead or alive

Nor it cannot be both not dead not alive

1

all bacteria are micro organism

all  pathogen are micro organism .

in the question it is given which of the option is “LOGICALLY CORRECT “

NOT “MAY BE LOGICALLY CORRECT” FOR LOGICALLY CORRECT U HAVE TO CONSIDER ALL SITUATIONS .U R CONSIDERING ONLY TWO.

FOR THE XOR PART

CONC1    IS” SOME A  ARE B”

CONC 2   IS “ALL A ARE NOT B “

NOW CONSIDER SETS A AND B

A HAVING 10 ELEMENTS

B HAVING 10 ELEMENTS

AND

A AND B  HAVING 5 ELEMENTS  COMMON (SO SOME ARE B) RI8? COMMON ELEMENTS

ALL A ARE NOT  B – OBVIOUSLY THERE EXIST SOME A WHICH IS NOT  B ...RI8?

NOW XOR OF THEM WILL YIELD 0

NOW FOR SATISFACTION AGAIN CONSIDER A CASE

WHERE B  IS SUSBET OF  A

….CONC 1 IS CORRECT

…...CONC  2   AGAIN IS CORRECT COZ THERE EXIST SOME A WHICH IS NOT IN A ,AS A IS THE SUPERSET .

AGAIN XOR GIVES 0

U HAVE IGNORED  BOTH CASES IN YOUR ANSWER

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@demalyaSEN

XOR won’t give 0

as xor is A∩B’ + A’∩B

Now for your second case Both conclusions hold true you’re right

But that again proves why D is wrong :D

0
Well what the proponents of option c say is absolutely right........since at least one of Conc-1 or Conc-2 has to be true for sure. The only issue is that a Conclusion of an argument is said to be correct(nothing to do with truthfulness of the  conclusion bcoz there can be a whole lot of other ways to conclude about the veracity of a statement ) only if it makes a deductive argument valid.well in this case note that the argument need not not even be sound( we say this when the implication is true but the premises not true)...., if it is inferrable from the argument alone....

For ex

St1: No mammal lays an egg

St2: Snake is not a mammal

Con1: Snake lays eggs

Con2 : Snake doesnot lay egg.

Now here it is quite obvious that one of Con1, Con2 has to be true since Con2 is negation of Con1, and it very much known to all that Con1 is true and Con2 is false.

(But)

Con1 (CONCLUSION -1, note the word conclusion )  is an incorrect conclusion of the argument just bcoz Con1 doesn't make the argument valid. Well here Con1 is being said to be an incorrect conclusion of the argument despite the fact that Con1 is true, just for the  reason that it doesnot make the argument valid

Similarly,

Con2(Conclusion-2) is an incorrect conclusion of the argument just bcoz Con2 doesnot make the argument valid.

Well the only thing is that correctness of a Conclusion is being confused with truthfulness of a conclusion and it is this that I'm trying to point out. Correctness of conclusion is spoken of in the context of an inductive argument / deductive argument.
0

@aniketh317

I agree

Being valid is not equal to truthfulness of the conclusion

But consider this

Take any single case like pathogen and bacteria are subsets superset or disjoint sets

Atleast One of the conclusions will be valid and true in that case.

A conclusion might be valid in one case but might not be in other

That is the basis of this question

You don’t need validity of conclusion in all cases

But take any case I guarantee you one of the conclusion will stay valid

The word Either makes a lot of difference

A coming to other options

They don’t even come close to being valid

0
bro am not talking about xor of sets am talking about xor of conclusions which is either T or Falways
0

tbh lets wait for answer key
0
The Con1, Con2  mentioned in the question are propositions whose truth values have been established by biologists/zoologists or who so ever is concerned with the taxonomy of microorganisms. Frankly speaking, nothing to do with cases and all that too 😆😆... The whole thing is about inferring the truth value of a conclusion from the given premises. Conclusion is correct in an argument only if I can infer that the truth value of the conclusion is true from the statements mentioned in the premises.

On a side note, in the stated answer:

All pathogens are not bacteria in English should have been :

Ǝx(pathogen(x) and not(bacteria(x))

Well the proposition that is given in the main answer translates to :

No pathogen is a bacteria.

Well I know that this is not a game changer 🤣🤣 mentioning it just for the sake of it..
0
bhai in simple words when  bacteria set and  pathogen set is intersecting both conclusions are true ,either or demands for only one  conclusion to be  true  but n this case both r true  busting the  argument for either or .conclusion 1 is noobish to understand .Conclusion 2 says all pathogens are not bacteria bro that is obvious .,all b acteria are not  pathogens and all pathogens are not bacteria ..am considering the intersection case only .please read through the comments u will get it .Don’t reverse engineer your answer
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@debmalyaSEN why are you considering Either as XOR?

It can also mean OR

0

bro i have provided u links .still am saying again ..

either or means one  condition will be true every time

.it is false if both conditions  are true

or

both conditions are false.

in  a race either you or i can win

it means

you win i lose

you lose i win

---not ----

you lose i lose

you win i win

coz only a single winner is required .

what you are saying is .. (OR)   NOT ( EITHER OR)

1
Another thing 🤣🤣

Ǝx(pathogen(x) and not(bacteria(x))

and

Ǝx(pathogen(x) and (bacteria(x))

are 2 propositions which don't assume False truth value simultaneously, only if we are convinced that the domain of discourse(the set of micro-organisms) is a non--empty set... which is not given in this stupid question anyway... so it seems to me that  there are hell lot of ways to challenge for D 🤣🤣🤣
2

Could you make a detailed pdf that can be used to challenge the answer key. All can refer and make changes and challenge it along with any references if any

1
@arjun sir please provide a valid solution so that we can challenge this ques
0
1. key providers requested to kindly update the solution for this one to neither, nor.
1. Graph theory Articulation point one too
2. And Sender Window size problem range extended to (50-52)

Requesting key providers to kindly incorporate the afore-mentioned changes

0
aniketh its already done on GO key
0
Ok thanks...
1

Why I think answer is D?

In such type of questions when a conclusion is given based on some statements then for that conclusion to be correct it must be true for all the cases.

But in this question we have a counter example where conclusion 1 fails and we also have a counter example where conclusion 2 fails , so we can say neither of the conclusion is correct because they are not true for all the cases.

Now if you take all the cases then you will see that either conclusion 1 is followed or conclusion 2 is followed but we can’t say that “either conclusion I or II is correct” because for any conclusion to be correct it must be true for all the cases. So option C is wrong.

All we need to refute a conclusion is a counter example in which both the statements are correct but conclusion is false.

Conclusion 1 states that some pathogens are bacteria, but the first venn diagram refutes that.

Conclusion 2 states that all pathogens are not bacteria, but the second venn diagram is against that.

Both the venn diagram follow from the original statements, so we have shown a counter example to both conclusions so option D is correct.

Option C is wrong as it doesn’t say by any means that both statements can’t be correct at the same time.

edited by
4
Answer is c either or one as not all and some boils to tautology,
1
Why can’t there be a scenario where pathogens is a subset of bacteria? In which case, neither conclusion holds for sure.
0
Yes you are correct
0
but in diagram 3 conclusion1 is getting true

so in any diagram either of the statement getting true
2
I don’t thing we can conclude based on 1 diagram, conclusion should be true in all cases.
1
yes that’s what all the cases are saying that in any case either of the conclusion can be correct.
0
Still you can say some pathogens are bacteria and vice versa what's the problem @pritisch
0
why can’t  pathogen be a superset of bacteria?

if pathogen is a superset of bacteia then

both conclusion are true ri8 ?
0
@debmalyaSEN A conclusion will be true if it is true in all diagrams, we just need a counter example to deny a conclusion.
0
Answer should be C as either conclusion 1 can be true or conclusion 2 can be true at any time but not both. Hence at any point of time atleast 1 of them has to hold.
1
No conclusion is correct, there are counter examples for them all, we can’t say either of them is correct and it is not mentioned in C that both can’t be correct at the same time.
0
zxy123  bro are u damn sure?
0
zxy just explain ur answer with more writing ,it will be claear
0
0
I’ll do just that then
0
The answer should be C. “Neither Nor” means that both are incorrect always, which is not true.
2
The question is asking whether we can come to conlusion 1 or conclusion 2! But we have counter example where both the conclusion are not true ! In that case we cannot come to any conclusion!  Both need not be incorrect always, but there ia a scenerio whether both the conclusions are not correct! Thus for me D is the correct answer!
0
Only the answer key can settle this now ¯\_(ツ)_/¯
0
@zxy123 i think i am pretty sure it will be neither nor.
0
Please see the venn diagram

We don’t know for sure which venn diagram is referred

Both the conclusions are contradictory

If you consider I correct then two is automatically false

If you consider II correct then one is automatically false

Both true and both false can never be the case

Therefore atleast one of them has to be correct
0
Dude... lol indeed
1
I have solved this problem by interpreting it as a syllogism question if you use standard procedures from Arun Sharma books the answer should be D, but if you interpret it as a First-order logic question one can see why option c could be possible. The answer will depend on how you interpret the question, I don't think option D is wrong if you see it as a syllogism question.

Here is the question explained with another example which will hopefully help people think freshly without thinking about the actual question.

Statement 1 – all rats who lost one of their limbs are 3 limb mammals
Statement 2 – all rodents who lost one of their limbs are 3 limb mammals
Conclusion 1 – some 3 limb rats are 3 limb rodents
Conclusion 2 – all 3 limb rats are not 3 limb rodents

Cases possible from given statements 1 and 2:

Now,

1. can we conclude that SOME 3 limb rats are 3 limb rodents? No. Counter example is figure 1

2. can we conclude that ALL 3 limb rats are not 3 limb rodents? No. Counter example is all other figures.

So neither conclusion 1, nor 2 is correct. There is no ambiguity here right? because neither of the conclusions were derivable from the premises.

-------------------------------------------------------------------------------------------------

Now why is – either conclusion 1 or 2 is correct – wrong? The answer lies in interpretation of the question (semantics), as well as the definition of a conclusion.

Saying that either conclusion 1 or conclusion 2 is correct implies that one of the above conclusions can possibly be deduced from the statements, meaning either we were able to deduce that some 3 limb rats are 3 limb rodents, or we were able to deduce that all 3 limb rats aren’t 3 limb rodents.

Definition of the conditional statement from Rosen which mentions what is called a “conclusion” :

Let p and q be propositions. The conditional statement p → q is the proposition “if p, then
q.” The conditional statement p → q is false when p is true and q is false, and true otherwise.
In the conditional statement p → q, p is called the hypothesis (or antecedent or premise)
and q is called the conclusion (or consequence).

Another definition from https://www.britannica.com/topic/logic#ref535920

“An inference is a rule-governed step from one or more propositions, called premises, to a new proposition, usually called the conclusion. An inference rule is said to be valid, or deductively valid, if it is necessarily truth-preserving. That is, in any conceivable case in which the premises are true, the conclusion yielded by the inference rule will also be true.”

Stmt 1 AND Stmt 2 → Conclusion 1 stmt ?   – False

Stmt 1 AND Stmt 2 → Conclusion 2 stmt ?   – False

But do the individual statements of conclusion 1 and conclusion 2 together form a tautology? Definitely.

Although here is where we need to differentiate between making a whole new proposition by interpreting option c as “stmt C1 OR stmt C2”, and what the logical english interpretation of the options should be, i.e. either conclusion one can be deduced or conlusion two can be deduced. (a conclusion being correct implies that the conclusion CAN be deduced. Refer the definitions above).

But we clearly can’t deduce either of the conclusions from the given premises. There is a clear difference between saying “one of the conclusion holds and is correctly deduced” vs “one of the statements of both the conclusions has to be true”, the 2nd one being an assertion, which doesn’t take into account what a conclusion is! and simply considers both conclusions as statements OR’ed together, which we shouldn’t implicitly assume.

I feel like my argument is sound, and I’m not dismissing the fact that the other way of interpretation of the question may have some merit to it. (don’t come after me @Nikhil_dhama, blame the english language), but either option D should be correct, or both option C and D should get marks. The case where only option C is correct is clearly wrong.

---------------------------------------------------------------

EDIT 1: As pointed out by @debmalya, statement of conclusion 2 “All pathogens are not bacteria” is probably being wrongly interpreted by everyone.
For example when we say that “All students are not toppers”, we don’t mean to say that there are no students who are toppers. Instead we mean that most of the students are not toppers.

Therefore the venn diagram of conclusion 1 and conclusion 2 both are actually identical, and they are not mutually exclusive, i.e one is not the negation of the other, and therefore both of them together in fact dont form a tautology, making option D the only correct choice.

edited by
4

Considering the 2nd statement ..  ”All pathogens are not bacteria”

by this i  mean  there exist some pathogens that is not bacteria

this is similar to a statement like “ALL students are not toppers”

by  this we mean there exist some student who is not topper ,do we mean that for every  element in the universe if it’s a student then it’s not the topper .no ri8

considering another example

”All chefs are not masterchefs”

by this i mean there exist some chef who is not a masterchef

by this we don’t mean  for every person in the universe if it’s a chef then he is not a masterchef .

considering another example

ALL STONES ARE NOT WORTHY

THIS MEANS  ATLEAST THERE EXIST SOME STONE HICH IS NOT WORTHY

IT DOESN’T MEANS..FOR EVERY OBJECT IN THE UNIVERSE IF ITS A STONE THEN IT’S NOT WORTHY

@rish-18 please understand what i am saying ,the way in which nikhil dhmma is interpreting 2nd statement is wrong

1
Yes i got what you are saying. Thanks for pointing it out. We should make a solid unambiguous and foolproof case incase the answer key doesnt come out in our favour!
2

The below two links support your argument.

Search for the following question:

Q. All students are not genius concludes that:

A. no student is genius

B.  all geniuses are students

C.  many students are not genius

D.  None of these

Answer given is option C and not A.

https://www.examrace.com/NTA-UGC-NET/NTA-UGC-NET-Objective-Questions/Paper-I-Sample-Questions/Teaching-And-Research-Aptitude-UGC-Paper-1-Part-25.amp.html

I think this fact conclusively proves that option D is the correct answer!

2

https://studysite.org/Discuss/Question/all_students_are_not_geniuses_concludes_that-83114066.htm

same thing ..

moreover ,consider a situation in which we have 500 microorganism   out of which  200s are bacteria and 200s are pathogen .100 both pathogen and bacteria .

considering situation when they r intersecting

Now if i say “all pathogens are not bacteria”   its trivial right .coz there are 200 pathogens which are not  bacteria .

now if i say  for all elements in universe if it’s a pathogen then it’s  not a bacteria ,this will  always yield false ..coz 100 micro organism are  both pathogen and bacteria  and infact this will yield only true when number of bacteria =no of pathogens  or in a situation when  bacteria is a superset of pathogen ..But we won’t go into that our primary aim is to prove”” either” wrong .

And now let us consider what nikhil dhamma is saying is correct then  again i will take a situation in which bacteria is a superset of pathogen .then according to his logic conc 1 is correct as  some pathogens are bacteria .Now according to him only    --for every element in the universe if it’s a  pathogen then it’s a bacteria is  also true .Again conclusion 1 xor conclusion 2 =0

0
someone please call  @arjun sir and show him these arguments
6
Well none of these arguments are needed. The only question is about the interpretation of the word "either or" and "neither nor". The way the options are formed the question setter must have had option C in his mind. Playing with such English usage is not good. Please post this question in cs.stackexchange and get good responses to show that this question is debatable. Options C and D should be given marks.
1

@Arjun sir, and for anyone else who wants to follow up on this question:

https://math.stackexchange.com/questions/4034468/interpreting-english-either-or-when-approaching-logical-deductions-doubt

As of now there are no answers on it, lets wait and see what people in the mathematics community have to say about this question.

1
Yes. 99% they will publish answer as C. Lets see if someone can give a formal argument to make them change this.
0
Just out of curiosity, which option do you personally lean towards using logic/reasoning?
0

well 4 answers so far..some saying ambiguous  ,and few saying either or can’t be tautology ..

well though quora is not a credible source ..https://www.quora.com/The-statement-All-A-are-not-B-related-to-syllogism-is-equivalent-to-which-of-the-following-sentences-No-A-is-B-or-Some-A-is-not-B

they are trying to say what all a ae not b means

2

@Arjun sir, can you please look over my argument once?

I will be challenging in case the answer key gives option c as correct.

2
will make a strong case against option c and will challenge it .

.I still  can’t understand why people are still saing option c….

anyway would love to learn from @arjun sir why is he inclining towards option c .

i have countered their argument with examples ,but they haven’t countered any of our argument ..

even in  stack exchange people are saying can’t be tautology .

people are confusing exor eith or .

i have shown what All A not B means ...many times . i have proved that the way nikhil is interpreting is wrong,through examples .

We have drawn venn diagrams ,have shown situations where it fails .

we have  shown that it is mentioned in the question  whether “ logically valid “  not  “may be logically valid”..we have to satisfy all cases .

if all these are not convincing i don’t know what more i have to do to prove d right .

will definitely challenge this question
1
had given my all ,to prove it .Hopefully the best answer will win
1
@Arjun sir you said 99% option C will be correct. I want to challenge this ques could you please provide a valid solution that can be used in this case.
0
If the answer key gives C as correct, won’t that be at the time the challenge time window is closed? If so, how will you re-challenge the question?

The only fair outcome is if both C and D are marked correct by the committee. One can only hope that will be the case.
2
1. Only conclusion I is correct
2. Only conclusion II is correct
3. Either conclusion I or II is correct  – does this imply options A and B and if so one can straight away ignore them and mark this or option D
4. Neither conclusion I nor II is correct

The bold marked line itself is a clue as to what the question setter would have had in his mind. I can only think that someone copied this question from somewhere and gave a different interpretation :) More discussion here: https://math.stackexchange.com/questions/4034468/interpreting-english-either-or-when-approaching-logical-deductions-doubt

Answer will be D only.

For C could be correct if

Some pathogens are NOT bacteria.

All pathogens are bacteria.

I'm giving competitive exams for period of time and I'm sure they put not in all statement just to confuse people .

0
bro provide a credible source to prove otherise no one will acknowledge you

A lot of ambiguity around the question. Here’s my take:

EITHER, what does it mean?

Found some articles comparing it to XOR

Either A or B

This means either A can be true OR B can be true, both can’t be true together and can’t be false together

https://math.stackexchange.com/questions/68333/what-is-the-logical-connective-for-either-or

https://english.stackexchange.com/questions/95559/can-either-mean-both-any-and-both

https://thewritepractice.com/how-to-use-either-neither-or-and-nor-correctly/

For this context, either conclusion 1 has to be true OR conclusion 2 has to be true

But for cases where either bacteria is a subset of pathogens or pathogens is a subset of bacteria or both are equal (while all being microorganisms), these are three valid possible conclusions, which are outside of the consideration of the provided conclusions

So we have options other than conclusion 1 or 2, because of which, we CAN’T say either one of them is true, both of them can be false, which can’t be allowed as per the meaning of EITHER-OR

So, NEITHER 1 nor 2 is NECESSARILY correct

Thus, D.

I don't know why answer c is wrong the guy above itself give answer is c though he write d some times first diagram true and sometime below two will be true so we can infer easily that either or will be true , where is the problem,it's quite trivial to see .

The answer will definitely change to c I am sure in this regard

edited
3

The problem is option C says “either is correct” which translates to “atleast one conclusion is correct”.

Neither conclusion is correct because for a conclusion to be correct, it has to be correct in all cases

1
bhai answer d ri8
0
Ok may be I am wrong ,but tha would be true only if conclusion has static behaviour i.e only one preposition is inferred but if we get flexibility then??
0

C would have been correct if it had said “either conclusion can be correct”. Then we will consider sub-cases where a conclusion is correct.

2
Give one scenario where both of them are incorrect. Either-Or is supposed to be considered as OR gate. If any of the conclusions hold, then the statement that either I or II is correct is overall true. But for Neither-Nor, it will be like NOR gate. That is, neither of them should be true in any case. This is clearly not possible, No matter what venn diagram you draw, either Some pathogens will be bacteria OR All pathogens won’t be bacteria. There can’t be any case, where both of them are false together. Therefore, the answer should be C.

Either Conclusion I or II is correct.
0
In case of All pathogens are bacteria!!!!

Both conclusions are false .because first says some pathogens are bacteria which is false.

Other one says all pathogens are not bacteria ..this is also false..for me D is correct
0
if all pathogens are bacteria ,does it imply soome pathhogens are bacteria?
0
@debmalyaSEN yes, for all--> there exists
0

A lot has been said about this question already. I guess I would have been onboard with option C if it had said “Either one is correct but not both”. Now let us see what GATE ans key says.

https://math.stackexchange.com/questions/2130327/does-either-make-an-exclusive-or

It’s hard to say whether “either or” is inclusive or exclusive. According to these answers, inclusive-or is far more common and is the convention. If GATE setters had written as “either I or II is true” (some sort of emphasis) then also it would have unambiguously meant exclusive or.

In contrast, “neither nor” unambiguously translates to (not A and not B) [can use deMorgan’s laws to check].

1 vote

Let’s end this :D

In the question

• Conclusion I:Conclusion I: Some pathogens are bacteria.
• Conclusion II:Conclusion II: All pathogens are not bacteria

There can be two possible cases

Consider Case 1

Where bacteria and pathogen are both subsets of microorganisms &

Bacteria ∩ Pathogen = null

For this case

Conclusion I fails but conclusion II passes

So we rule out Option A & D

Consider Case 2

Where bacteria and pathogen are both subsets of microorganisms &

Bacteria ∩ Pathogen = not null

For this case

Conclusion I passes but conclusion II fails

So we rule out Option B now

Now the question doesn’t say if its OR or XOR

and only conclusive logic we can derive is XOR

So C satisfies either one of the conditions at a time

It can never satisfy both or none cause its like

Schrödinger's cat experiment

The cat can either be alive or dead

It cannot be both dead or alive

Nor it cannot be both not dead not alive

So Final ANSWER C :D

Please fell free to try to correct a question which you definitely messed up. :D

2
It’s answer should be C only there is no way to falsify both conclusion at same time .
0
I_am_winner if you find a good solution then please paste here too I want to challenge too
1
I will also need if we get proper reasoning brother.Anyway please share anything you get .

Everyone is debating over C and D,

Option C: Either conclusion I or II is correct.

Remember when pathogens and Bacteria Intersects. Both the conclusions hold..therefore C cannot be the answer...D is correct
0
In all the possible cases either 1 occurs or 2 occurs or both occurs .

So neither 1 nor 2 is also false .
0
What do you think? What does Either or mean?
0
Obviously Either or means only one should happen .

So it is either or is not correct answer .

But also neither nor is not correct

U have seen ECE question of same type ?
1

Yes bro I’ve looked at the question asked in ECE, Both questions are completely different.

ECE Question is

• Statement 1Statement 1: All purple are green.
• Statement 2Statement 2: All black are green.

• Conclusion IConclusion I: Some black are purple.
• Conclusion IIConclusion II: No black is purple.

Answer is C Either conclusion II or IIII is correct.

Now read the conclusion II of CS and ECE. There is huge difference.
In case of ECE both conclusions cannot hold at the same time. But its happening in case of question asked in Set 1..Just try and draw ven diagram of both questions..you will understand..I dunno how to draw ven diagram here..

When you take the intersection of purple and green..you will notice only conclusion one will be true, conclusion 2 will be false..hence C is the answer but in the case of the question asked in CS when we draw ven diagram you will notice both are true which is not allowed in either or…

Just a small thing i want to say don’t try and apply much of mathematics and dive into this question. If you ask the same question from people who prepare for govt exams they will always say D is the correct answer, I dunno why people are complicating this question like anything when this question can be solved in less than 30 seconds..and straight away most of the answers can be eliminated…

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