Let p, q, r be three statements such that the truth value of (p [ ] q) [ ] ([ ]q [ ] r) is…

Question

Let p, q, r be three statements such that the
truth value of
(p $$ \wedge $$ q) $$ \to $$ ($$ \sim $$q $$ \vee $$ r) is F. Then the
truth values of p, q, r are respectively :

Accepted Answer

Given, (p $$ \wedge $$ q) $$ \to $$ ($$ \sim $$q $$ \vee $$ r) is false.

This statement is false when

p $$ \wedge $$ q = T

and ($$ \sim $$q $$ \vee $$ r) = F

Now, p $$ \wedge $$ q = T when

both p and q are True.

As q = T

$$ \therefore $$ $$ \sim $$q = F

Now, ($$ \sim $$q $$ \vee $$ r) = F when

r = F as $$ \sim $$q is already false.

$$ \therefore $$ p = T

q = T

r = F

Solutions · 1