The number of ordered triplets of the truth values of $$p, q$$ and $$r$$ such that the truth value of the statement $$p \vee q \wedge p \vee r \Rightarrow q \vee r$$ is True, is equal to _______

We need to find the number of ordered triplets $$(p, q, r)$$ of truth values such that $$p \vee (q \wedge (p \vee r)) \Rightarrow (q \vee r)$$ is True.

An implication $$A \Rightarrow B$$ is False only when $$A$$ is True and $$B$$ is False.

When is the consequent False?

$$q \vee r = F$$ requires $$q = F$$ and $$r = F$$.

With $$q = F, r = F$$, evaluate the antecedent:

$$p \vee (F \wedge (p \vee F)) = p \vee (F \wedge p) = p \vee F = p$$

So the implication is False only when $$p = T, q = F, r = F$$.

Total possible triplets = $$2^3 = 8$$. Number where implication is False = 1.

Number where implication is True = $$8 - 1 = 7$$.