1. The problem involves understanding the logical conjunction (AND) operation $p \wedge q$ for two propositions $p$ and $q$. 2. The truth table for $p \wedge q$ is given with $p$ and $q$ each being either True (V) or False (F). 3. The rule for conjunction $p \wedge q$ is: it is True only if both $p$ and $q$ are True; otherwise, it is False. 4. From the table: - When $p = V$ and $q = V$, $p \wedge q = V$ (True). - When $p = V$ and $q = F$, $p \wedge q = F$ (False). - When $p = F$ and $q = V$, $p \wedge q = F$ (False). - When $p = F$ and $q = F$, $p \wedge q = F$ (False). 5. The colored rectangles in the table visually represent the truth values: purple for True and blue or letter F for False. Final answer: The conjunction $p \wedge q$ is True only when both $p$ and $q$ are True; otherwise, it is False.