Answer
According to the truth table for $p\rightarrow q$, this statement evaluates to true when $p$ is false or $q$ is true. Therefore, we can rewrite it as $\neg p\lor q$. Using the same basic equivalence, we can write $\neg q\rightarrow\neg p$ as $\neg\neg q\lor \neg p$. We use the double negation principle to reduce $\neg\neg q$ to $q$ and end up with $q\lor \neg p$. Since disjunctions are commutative, we can rewrite this as $\neg p\lor q$, which is the same as the simplified version of $p\rightarrow q$. Since each proposition can be simplified to the same expression, the two propositions are equivalent.
Work Step by Step
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