1. The problem asks us to determine the truth values of the statements based on the given predicate $P(x)$. 2. For the first predicate $P(x)$: "$x \leq 4$". 3. Evaluate each part: a) $P(0)$ means $0 \leq 4$, which is true. b) $P(4)$ means $4 \leq 4$, which is true. c) $P(6)$ means $6 \leq 4$, which is false. 4. For the second predicate $P(x)$: "The word $x$ contains the letter 'a'." 5. Evaluate each part: a) $P(\text{orange})$ means "orange" contains 'a', which is true. b) $P(\text{lemon})$ means "lemon" contains 'a', which is false. c) $P(\text{true})$ means "true" contains 'a', which is false. d) $P(\text{false})$ means "false" contains 'a', which is true. Final answers: - For $P(x) = x \leq 4$: a) true, b) true, c) false. - For $P(x)$ = "word $x$ contains 'a'": a) true, b) false, c) false, d) true.