P : prices are raised
W : wages are raised
I : there is inflation
C : Congress must regulate inflation
S : people will suffer
U : Congressmen will be unpopular
Premises :- ((W V P) → I), (I → (C V S)), (S → U), (C’ $\wedge$ U’)
Conclusion :- W’
Valid Argument :- If all the premises are true, then the conclusion must be true. If it is possible to make all the premises true and the conclusion false, then the argument is invalid. But if it is impossible to make all the premises true and the conclusion false, then the argument is valid.
Let’s take conclusion as false and try to make all the premises true.
Conclusion is false => W’ $\equiv$ False => W is true.
1st Premise is true => ((W V P) → I) $\equiv$ True => ((True V P) → I) $\equiv$ true => (True → I) $\equiv$ true => I is true.
4th Premise is true => (C’ $\wedge$ U’) $\equiv$ True => C’ $\equiv$ true and U’ $\equiv$ true => C is false and U is false.
2nd Premise is true => (I → (C V S)) $\equiv$ True => (true → (false V S)) $\equiv$ True => S is true.
3rd Premise is true => (S → U) $\equiv$ True => but it is impossible because S is true and U is false. So, S → U is false.
So, it is impossible to make all the premises true and the conclusion false. Therefore the argument is valid.
Also we can say ((W V P) → I)$\wedge$(I → (C V S))$\wedge$(S → U)$\wedge$(C’ $\wedge$ U’) → W’ is tautology.
Ans is A,C.
