To evaluate the truth value of $(p \vee q) \Rightarrow \neg p$, let's analyze it using truth values of $p$ and $q$.

Step-by-Step Solution

1. Expression Analysis:

   • $(p \vee q)$ represents the logical "or" of $p$ and $q$, which is true if at least one of $p$ or $q$ is true.
   • $\neg p$ represents the negation of $p$, which is true when $p$ is false.

2. Implication Analysis:

   • The implication $(p \vee q) \Rightarrow \neg p$ will be true unless $(p \vee q)$ is true and $\neg p$ is false.
   • The implication is only false when the antecedent $(p \vee q)$ is true and the consequent $\neg p$ is false.

3. Truth Table:

Let's construct a truth table to evaluate the expression for all possible values of $p$ and $q$.

$p$	$q$	$p \vee q$	$\neg p$	$(p \vee q) \Rightarrow \neg p$
T	T	T	F	F
T	F	T	F	F
F	T	T	T	T
F	F	F	T	T

4. Result:
   • The expression $(p \vee q) \Rightarrow \neg p$ is false when $p$ is true (whether $q$ is true or false).
   • Therefore, the truth value of the expression is False.

Answer

The correct answer is:

• False

Would you like additional details or explanations?

Here are some related questions for practice:

1. What is the truth value of $(p \wedge q) \Rightarrow p$?
2. Evaluate $(p \Rightarrow q) \Rightarrow (\neg q \Rightarrow \neg p)$ using a truth table.
3. Determine the truth value of $\neg(p \vee q) \Rightarrow \neg p$.
4. For which values of $p$ and $q$ is $(p \vee \neg q) \Rightarrow (q \Rightarrow p)$ true?
5. Explain how the truth table changes when using an exclusive OR instead of inclusive OR.

Tip: For any implication $(A \Rightarrow B)$, remember that it’s false only when $A$ is true, and $B$ is false.