the contrapositive of `p implies q` is ......

Answer

To determine the contrapositive of the statement "p implies q" (denoted as \( p \implies q \)), we follow these steps:

1. **Understanding the Implication**: The statement \( p \implies q \) means "if p is true, then q is also true."

2. **Negating the Statements**: To find the contrapositive, we need to negate both the hypothesis (p) and the conclusion (q). This means we will consider "not p" (¬p) and "not q" (¬q).

3. **Reversing the Implication**: The contrapositive involves reversing the implication. Instead of "if p, then q," we will express it as "if not q, then not p." This means we will write it as \( \neg q \implies \neg p \).

4. **Final Statement**: Therefore, the contrapositive of the statement \( p \implies q \) is \( \neg q \implies \neg p \).

Thus, the contrapositive of \( p \implies q \) is \( \neg q \implies \neg p \).

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