The proposition p↔q  is equivalent to (¬p ∨ q) ∧(¬q ∨ p)  Group startsTrue or FalseTrue, unselectedFalse

Break Down the Problem

1. We need to determine if the proposition $p \leftrightarrow q$ is equivalent to $(\neg p \lor q) \land (\neg q \lor p)$.
2. This involves analyzing both expressions and checking if they yield the same truth values.

Relevant Concepts

• The biconditional $p \leftrightarrow q$ states that $p$ is true if and only if $q$ is true. This means both $p$ and $q$ must have the same truth values.
• The expression $(\neg p \lor q)$ is true unless $p$ is true and $q$ is false.
• The expression $(\neg q \lor p)$ is true unless $q$ is true and $p$ is false.
• The conjunction $\land$ means both sides must be true for the whole expression to be true.

Analysis and Detail

1. Truth Table Creation:
   • We will create a truth table for both $p \leftrightarrow q$ and $(\neg p \lor q) \land (\neg q \lor p)$.

2. Comparison of Results:
   • From the truth table above, we see that both $p \leftrightarrow q$ and $(\neg p \lor q) \land (\neg q \lor p)$ yield the same truth values across all combinations of $p$ and $q$.

Verify and Summarize

• Since both expressions have the same truth values in every case, we can confirm that they are logically equivalent.

Final Answer

The proposition $p \leftrightarrow q$ is equivalent to $(\neg p \lor q) \land (\neg q \lor p)$; thus, the statement is True.