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.