1. The problem is to understand the logical expression $$\forall x (P(x) \lor F(y))$$. 2. This expression means "For all values of $x$, either $P(x)$ is true or $F(y)$ is true." Here, $y$ is a fixed variable, not quantified. 3. The universal quantifier $\forall x$ applies to the entire statement inside the parentheses. 4. The logical OR ($\lor$) means that for each $x$, at least one of $P(x)$ or $F(y)$ must be true. 5. Since $F(y)$ does not depend on $x$, if $F(y)$ is true, then the whole statement is true regardless of $P(x)$. 6. If $F(y)$ is false, then $P(x)$ must be true for every $x$ for the statement to hold. 7. Therefore, the expression is logically equivalent to $$F(y) \lor \forall x P(x)$$. Final answer: $$\forall x (P(x) \lor F(y)) \equiv F(y) \lor \forall x P(x)$$.