Ans : A B D
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)
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
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.