The question asks you to use a truth table to determine which of the following statements is equivalent to $p \lor (p \land q)$. The options are:

1. $p$
2. $\neg p \lor \neg q$
3. $\neg q$
4. $p \lor q$

Step-by-Step Solution:

Expression: $p \lor (p \land q)$

Using the distributive property of logic: $p \lor (p \land q) = p$ This is because $p \land q$ will always be true when $p$ is true, and $p \lor (anything)$ simplifies to $p$.

Let's verify using a truth table:

As seen, the column for $p \lor (p \land q)$ is identical to the column for $p$. Therefore, the statement $p \lor (p \land q)$ is logically equivalent to $p$.

Correct Answer: $p$ (Option 1)

Would you like more details or have any questions?

5 Related Questions:

1. What is the distributive property in propositional logic?
2. How does $p \land q$ affect the expression $p \lor (p \land q)$?
3. Can truth tables be used for more complex logical expressions?
4. What other logical equivalences can simplify expressions?
5. What is the relationship between conjunction ($\land$) and disjunction ($\lor$) in logic?

Tip:

When simplifying logical expressions, always check for common logical identities like distributive, associative, and commutative properties to make your work easier.