1. The problem is to create a truth table for the logical AND operation between two propositions $p$ and $q$. 2. The AND operation, denoted as $p \wedge q$, is true only when both $p$ and $q$ are true. 3. The truth table lists all possible truth values of $p$ and $q$ and the result of $p \wedge q$: $$\begin{array}{c|c|c} p & q & p \wedge q \\\hline \text{True} & \text{True} & \text{True} \\ \text{True} & \text{False} & \text{False} \\ \text{False} & \text{True} & \text{False} \\ \text{False} & \text{False} & \text{False} \end{array}$$ 4. Explanation: The AND operation outputs true only if both inputs are true; otherwise, it outputs false. This completes the truth table for $p \wedge q$.