GO Classes 2024 | Weekly Quiz 7 | Propositional Logic | Question: 13

Answer 1

Statement $136$ is true. All others are false.

Comments

How?

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I don’t know my approach is correct or not but i did this way.

here suppose we assume that S1 is true Then it meaning is that exactly One statement in the list is false. Here we assumed S1 as true so it can’t be false. Remaining 136 will be true. Here at a time all the 137 statements can't be true cause we know that only One statement is false.

CASE 1: suppose S2 is false then remaining all the statements will be true. So S3 will be true but here according to S3 exactly 3 statements are false and according to S1 exactly 1 statements are true. here its conflicting.

CASE 2: suppose S3 is false then  remaining all the statements will be true. So S2 will be true but here according to S2 exactly 2 statements are false and according to S1 exactly 1 statements are true. here also its conflicting

CASE 3: suppose any other statement except S2 and S3 is false. Then also it will conflict with S1.

So in conclusion S1 can't be true cause if we assume that S1 is true then it will create conflict with other statements.

If you do like this then you will find that if we assume that particular statement is true then it will create conflict with other statement.

But for S136 its not the case. If we assume that S136 is true then it means Exactly 136 statements are false. Only one statement is true And that one statement we already assume true which is S136. So no other element than S136 is true. So there are no such statements which create conflict.

So after assuming S136 as true , there are no such statements which can create conflict. So S136 can be true. So in the list of 137 statements , only statement S136 is true.

Am I right @Deepak Poonia sir ???

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https://www.youtube.com/watch?v=vgqUISdGbvk

I found this explanation helpful. Check this out.

@Deepak Poonia Hi sir, thanks for giving this question. Is the explanation in this video correct one? Can you please check once if possible?

Answer 2

go options wise and try to eliminate them 

A : no statement true

this means S137 = T but this contradicts option A 

B : all statements true 

these are exactly statements, each statement if True makes other statements false immediately

C : >1 statement true

from similar logic of option B, this is false

there can be exactly n false statements at a time 

D : exactly 1 statement true

if u come down from S1 by assuming T one by one, they contradict each other

but as soon as u come to S136 = T → if this statement is true then rest 136 statements are False which makes S136 = T

Hence , true