If $$p \Rightarrow (q \lor r)$$ is False, then the truth values of p, q, r are respectively, (where T is True and F is False)

First, recall the logical rule for an implication. The statement $$p \Rightarrow s$$ is false only in one specific situation: when the antecedent $$p$$ is True (T) and the consequent $$s$$ is False (F). In every other combination the implication is True. Symbolically, we can rewrite an implication with the formula $$p \Rightarrow s \;=\; \lnot p \,\lor\, s,$$ which confirms the same fact because a disjunction $$\lnot p \lor s$$ fails exactly when $$\lnot p$$ is F (so $$p$$ is T) and simultaneously $$s$$ is F.

Now we apply this rule to the given compound statement $$p \Rightarrow (q \lor r).$$ Here the consequent is the disjunction $$(q \lor r).$$ We are told that the whole implication is False. Therefore, by the rule just stated, the following two conditions must hold together:

1. $$p$$ is True, because the antecedent must be True for the implication to fail.

2. $$(q \lor r)$$ is False, because the consequent must be False for the implication to fail.

Next, we analyse the disjunction $$(q \lor r).$$ A disjunction $$q \lor r$$ is True if at least one of $$q$$ or $$r$$ is True, and it is False only when both $$q$$ and $$r$$ are False. So, for $$(q \lor r)$$ to be False, we must have

$$q = \text{F} \quad \text{and} \quad r = \text{F}.$$

We already found $$p = \text{T}.$$ Putting these results together, the required truth values are

$$p = \text{T}, \qquad q = \text{F}, \qquad r = \text{F}.$$

Looking at the options, this matches Option A, which lists T, F, F in that order.

Hence, the correct answer is Option A.