1. **State the problem:** We have two statements: $p$: "The shop is open." $q$: "The shop is closed." We want to form a compound statement that represents a contradiction and verify it using a truth table. 2. **Understanding contradiction:** A contradiction is a compound statement that is always false regardless of the truth values of its components. 3. **Forming the compound statement:** Since $p$ and $q$ are opposite statements, the statement $p \wedge q$ ("$p$ and $q$") represents a contradiction because the shop cannot be both open and closed at the same time. 4. **Truth table for $p \wedge q$:** | $p$ | $q$ | $p \wedge q$ | |-----|-----|--------------| | T | T | F | | T | F | F | | F | T | F | | F | F | F | Explanation: - $p \wedge q$ is true only if both $p$ and $q$ are true. - Since $p$ and $q$ are contradictory, they cannot both be true. - Therefore, $p \wedge q$ is always false. 5. **Conclusion:** The compound statement $p \wedge q$ is a contradiction because it is false for all possible truth values of $p$ and $q$.