Write the converse of the inverse of p implies q.

Answer

To solve the problem of finding the converse of the inverse of the statement "P implies Q," we will follow these steps:

### Step 1: Understand the original statement
The original statement is "P implies Q," which can be symbolically represented as:
\[ P \implies Q \]

### Step 2: Find the inverse of the original statement
The inverse of a statement "P implies Q" is formed by negating both the hypothesis and the conclusion. Thus, the inverse of "P implies Q" is:
\[ \neg P \implies \neg Q \]
This means "If not P, then not Q."

### Step 3: Find the converse of the inverse
The converse of a statement "A implies B" is formed by switching the hypothesis and conclusion. Therefore, the converse of the inverse \(\neg P \implies \neg Q\) is:
\[ \neg Q \implies \neg P \]
This means "If not Q, then not P."

### Final Answer
The converse of the inverse of the statement "P implies Q" is:
\[ \neg Q \implies \neg P \]

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