If p [ ] (q [ ] r) is false, then the truth values of p, q, r are respectively :-

Question

If p $$ \Rightarrow $$ (q $$ \vee $$ r) is false, then the truth values of p,
q, r are respectively :-

Accepted Answer

p $$ \to $$ (q $$ \vee $$ r)

= $$ \sim $$ p $$ \vee $$ (q $$ \vee $$ r)

$$ \sim $$ p $$ \vee $$ (q $$ \vee $$ r) is false when

(1) $$ \sim $$ p = False $$ \Rightarrow $$ P = True

and (2) (q $$ \vee $$ r) is false $$ \Rightarrow $$ q and r both are false.

Solutions · 1