QuestionA biconditional statement, $p \leftrightarrow q$ , is true only when both $p$ and $q$ are true or both are false.

Studdy Solution

STEP 1

Assumptions1. We are dealing with a biconditional statement, denoted as $p \leftrightarrow q$ . . We need to find the condition under which this biconditional statement is true.

STEP 2

The biconditional statement $p \leftrightarrow q$ is defined as $(p \rightarrow q) \land (q \rightarrow p)$ , which means "if p then q" and "if q then p".

STEP 3

The implication $p \rightarrow q$ is true except for the case where $p$ is true and $q$ is false.

STEP 4

Similarly, the implication $q \rightarrow p$ is true except for the case where $q$ is true and $p$ is false.

STEP 5

Therefore, the biconditional statement $p \leftrightarrow q$ is true only when both implications are true, that is, when $p$ and $q$ have the same truth values.
In other words, a biconditional statement, $p \leftrightarrow q$ , is true only when both $p$ and $q$ are true or when both $p$ and $q$ are false.

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