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If either wages or prices are raised, there will be inflation. If there is inflation, then either the government must regulate it or the people will suffer. If the people suffer, the government will be unpopular. Government will not be unpopular. Which of the following can be validly concluded from the above statements.

  1. People will not suffer
  2. If the inflation is not regulated, then wages are not raised
  3. Prices are not raised
  4. If the inflation is not regulated, then the prices are not raised
  5. Wages are not raised
asked in Mathematical Logic by Loyal (6.9k points)
edited by | 456 views
0
let prices are raised - a

wages are raised - b

there will be inflation -c

government must regulate - d

people will suffer - e

government will be unpopular -f

 

Given stmts(premises)

a v b -> c =>premise1(p1)

c -> d v e =>premise2(p2)

e -> f =>premise3(p3)

~f =>premise4(p4)

 

there will be valid conclusion if p1 ^ p2 ^ p3 ^ p4 -> Conclusion

 

there should not be case such that conclusion is false and (p1 ^ p2 ^ p3 ^ p4 ) is false

 

But here in A OPTION, e is true, to make p3 true f should be true, but p4 will become false.

 

here there is a case T->F so not valid conclusion.

But answer given as A, how it is valid

3 Answers

+12 votes
Best answer
It is told in the question "If the people suffer, the government will be unpopular". And "government will not be unpopular" means, people will not suffer.
It is like A->B is true and ~B is given. So, ~A must be true.

So, (a) is valid (always true).

Lets take the English meaning

Government will not be unpopular

$\implies$ People will not suffer
$\implies$ Either no inflation or government regulates it
$\implies$ If no regulation then no inflation
$\implies$ if no regulation then no wage or price rise

So, (b) and (d) are valid (always true) and (c) and (e) are not valid.
answered by Veteran (342k points)
selected by
0
A is surely corrrect but what about B and D...For B,D, as people will not suffer(concluded) and government has not regulated the inflation(given in options) then it can be concluded that there is no inflation and hence no price/wages are raised....isn't it?
+1
@Shaun Patel : In option (b), if inflation is not regulated, then it is not necessary that wages are not raised, i.e. wages might have been raised, because then inf;ation would have occured, and still we could have said that inflation is not regulated, because then people will suffer.

Similar case for option (d). So option (b) and (d) are incorrect.
0
To put these things in English sentences is the mistake I commited..to ammend it, W=wages raised,P=price raised,I=Inflation occured,G=government regulates it,PS=people suffer,GU=government becomes unpopular....here are relations...(W+P)->I , I->(G+Pe) , Pe-> GU....with the statements we have concluded that people wont suffer (Pe=0)..as a result we left with (W+P)->I , I->G which is equal to (W+P)->G ...now, as given in the option B if we make value of G =0(not regulated) then both W and P has to be zero......thanks
+2

Lets take the English meaning

Government will not be unpopular

$\implies$ People will not suffer
$\implies$ Either no inflation or government regulates it
$\implies$ If no regulation then no inflation
$\implies$ if no regulation then no wage or price rise

In your statement, 
(W+P)->G
Now ~G -> ~W and ~P rt?

So, a, b and d are answers. I misread the first sentence earlier. That is why I posted only (a) as answer.


 

0
Yeap, that is what I meant...thanks
0
I believe it should not be in Easy category :)...Medium would suffice..just my observation
0
Yes. Its definitely normal difficulty for GATE :)
+1 vote

let the variable we use are 
W : wages are raised
P : prices are raised
I :  there is inflation
G : government must regulate it
S : people will suffer
U : government will be unpopular

"If either wages or prices are raised, there will be inflation" : (W+P)->I ...(1)
"If there is inflation, then either the government must regulate it or the people will suffer" : I->(G+S)  ...(2)
"If the people suffer, the government will be unpopular" : S->U  ...(3)
"Government will not be unpopular" : U'  ...(4)

options are :
A. "People will not suffer" : S'
B. "If the inflation is not regulated, then wages are not raised" : I'->W'
C. "Prices are not raised" : P'
D. "If the inflation is not regulated, then the prices are not raised" : I'->P'
E. "Wages are not raised" : W'

using (3) and (4) we get
S' ...(5)
which is option A so option A is Valid
from (1), we do contrapositive of it 
I'->(W+P)' = I'->(W'.P')= (I'->W').(I'->P') which is options B and D respectively so options B and D are also valid 

Hence options A, B and D are valid 
 

answered by Active (2.2k points)
0
if the inflation is not regulated then  wages are not raised and prices are not raised this should be true but in b and d cases they have given it separately correct if am wrong so according to me a should be only answer
0
Better answer ....
0 votes

Ans : A B D

Let 

W :  wages raised 

P : piece increased

I  :  There is inflation

R : Inflation Regulated by Govt.

S : People will suffer 

U :  government becomes unpopular

Lets Translate given information in Logic form

"If either wages or prices are raised, there will be inflation"           (W  V  P ) -----> I     (1)

"If there is inflation, then either the government must regulate it or the people will suffer"   I ---> (R V S)       (2)

"If the people suffer, the government will be unpopular"     S ---> U         (3)

"Government will not be unpopular"  ~U     (4)

Lets Derive 

A)

We know A--->B is same as ~B--->~A   It is called contrapositive.

hence S ---> U is same as ~U ---> ~S  

from (4)  we know ~U holds true. hence  ~U ---> ~S   gives  ~S i.e. People will suffer.

B,D)    Now in  I ---> (R V S)    (from eq 2)   'S'  becomes false 

Note A--->B becomes true  when (A,B) is (T, T) or (F, T) or (F, F)

now as S is now know to be false , and I option B they said "If the inflation is not regulated"

means R is false

if R is false then  (R V S) is false . then  to make   I ---> (R V S) true I must be False .( meaning   there is no inflation )

Now to make eq(1)     (W  V  P ) -----> I     true either W must be false or P must be false or both must be false

C,E)

In option B and D they specifically mentioned that Prices are not regulated , hence we took R as False

But for C , E it is not so. R can be true.

If R is true  then to make   I ---> (R V S)   true (Note that we have already seen S is false) 

I can be either true or false 

If I true 

then to make  (W  V  P ) -----> I  true . W & P can be either true or false

If I is false 

then to make  (W  V  P ) -----> I  true . W & P must be false

As you can see we get ambiguous answer for  W and P , hence  c and d are false.

answered by Junior (747 points)
edited by

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