TIFR CSE 2011 | Part A | Question: 1

Question

• 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.

• A. People will not suffer
• B. If the inflation is not regulated, then wages are not raised
• C. Prices are not raised
• D. If the inflation is not regulated, then the prices are not raised
• E. Wages are not raised

Comments

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

Answer 1

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.