Here is the detailed breakdown of the answers to each question based on the uploaded file:

Question 11:

Statement: $P(x)$ denotes $x \leq 4$.
Truth values of $P(4)$:

• $P(4)$: $4 \leq 4$ is True.
  Correct Answer: A. True

Question 12:

Statement: $P(x)$ denotes $x \leq 2$.
Truth values of $P(0) \land P(2)$:

• $P(0)$: $0 \leq 2$ is True.
• $P(2)$: $2 \leq 2$ is True.
• $P(0) \land P(2) = \text{True and True = True}$.
  Correct Answer: A. True

Question 13:

Statement: $P(x)$ denotes $x \leq 3$.
Truth values of $P(6) \lor P(5)$:

• $P(6)$: $6 \leq 3$ is False.
• $P(5)$: $5 \leq 3$ is False.
• $P(6) \lor P(5) = \text{False or False = False}$.
  Correct Answer: B. False

Question 14:

Statement: $P(x)$ denotes "The word $x$ contains the letter 'a'".
Truth values of $P(\text{Lemon})$:

• The word "Lemon" does not contain the letter 'a'. Hence, $P(\text{Lemon})$ is False.
  Correct Answer: B. False

Question 15:

Statement: $P(x)$ denotes $x + 1 > x$.
Truth values of $\forall x \, P(x)$ where the domain is all real numbers:

• For all real numbers $x$, $x + 1 > x$ is always True.
  Correct Answer: A. True

Question 16:

Statement: $Q(x)$ denotes $x < 2$.
Truth values of $\forall x \, Q(x)$ where the domain is all real numbers:

• For all real numbers, $Q(x) = x < 2$ is not true for every $x$ (e.g., $x = 3$ violates it). Hence, $\forall x \, Q(x)$ is False.
  Correct Answer: B. False

Do you have any specific parts you want me to explain in more detail or clarify further?

Related Questions:

1. What is the significance of universal quantification in logical statements?
2. How does logical conjunction ($\land$) differ from disjunction ($\lor$) in these problems?
3. Why is the truth value of $\forall x \, P(x)$ significant when the domain is all real numbers?
4. How can negation impact the interpretation of logical statements in such problems?
5. Could the truth values differ for $\forall x \, Q(x)$ if the domain was restricted (e.g., $x \leq 2$)?

Tip: Always verify whether a given statement applies to every element in the domain for quantifications like $\forall x$.