Let $p$ and $q$ be propositions. Which of the following logical expressions is equivalent to the implication $p⟹q$?

Solution

1. Construct the truth table for $p⟹q$.
2. The truth table shows $p⟹q$ is false only when $p$ is true and $q$ is false.
3. The expression $\neg p\vee q$ is false only when $\neg p$ is false (i.e., $p$ is true) and $q$ is false.
4. Since both have the same truth table, $p⟹q\equiv \neg p\vee q$.
5. Hence the answer is (A).