Let p, q, r be three statements such that the truth value of (p ∧ q) → (~q v r) is F. Then the truth values of p, q, r are respectively :

Question

Let p, q, r be three statements such that the truth value of (p ∧ q) → (~q \(\lor\) r) is F. Then the truth values of p, q, r are respectively : 

(1) T, F, T 

(2) F, T, F 

(3) T, T, F 

(4) T, T, T

Answer 1

(3) T, T, F

(p ∧ q) → (~q \(\lor\) r) = false

when (p ∧ q) = T

and  (~q \(\lor\) r) = F

So (p ∧ q) = T is possible when p = q = true 

\(\therefore\)  ~q = False (q = true) 

So (~q \(\lor\) r) = False is possible if r is false

\(\therefore\) p = T, q = T, r = F