1. The problem asks to express the exclusive disjunction $p@q$ using only negation ($\sim$), conjunction ($\wedge$), and inclusive disjunction ($\vee$). 2. By definition, $p@q$ means exactly one of $p$ or $q$ is true, but not both. 3. This can be expressed as: $$(p \wedge \sim q) \vee (\sim p \wedge q)$$ 4. Explanation: The formula states that either $p$ is true and $q$ is false, or $p$ is false and $q$ is true. 5. This uses only negation, conjunction, and inclusive disjunction as required. Final answer: $p@q \equiv (p \wedge \sim q) \vee (\sim p \wedge q)$