The statement $(p\vee q)\wedge (\neg p)⟹q$ is:

Solution

1. We start with the expression $(p\vee q)\wedge (\neg p)⟹q$.
2. Applying the distributive law to the antecedent, we get $(p\wedge \neg p)\vee (q\wedge \neg p)$.
3. Since $(p\wedge \neg p)$ is a contradiction ($F$), the expression simplifies to $F\vee (q\wedge \neg p)$, which is equivalent to $(q\wedge \neg p)$.
4. The full implication is $(q\wedge \neg p)⟹q$, which is a tautology because if $(q\wedge \neg p)$ is true, then $q$ must be true.
5. Hence the answer is (A).