Write the converse and contrapositive of implications:
if n is an even integer then it is divisible by 2

Answer

To solve the problem of writing the converse and contrapositive of the implication "If n is an even integer, then it is divisible by 2," we can follow these steps:

### Step 1: Identify the implication
The given statement can be expressed in the form of an implication:
- Let \( p \): "n is an even integer"
- Let \( q \): "n is divisible by 2"

Thus, the implication can be written as:
\[ p \implies q \]
This translates to:
"If n is an even integer, then n is divisible by 2."

### Step 2: Write the converse
The converse of an implication \( p \implies q \) is given by \( q \implies p \). Therefore, we need to switch the hypothesis and conclusion:
- The converse is:
"If n is divisible by 2, then n is an even integer."

### Step 3: Write the contrapositive
The contrapositive of an implication \( p \implies q \) is given by \( \neg q \implies \neg p \), where \( \neg \) denotes negation. This means we need to negate both the hypothesis and conclusion:
- The negation of \( q \) ("n is divisible by 2") is "n is not divisible by 2."
- The negation of \( p \) ("n is an even integer") is "n is not an even integer."

Thus, the contrapositive is:
"If n is not divisible by 2, then n is not an even integer."

### Summary of Results
- **Original Statement**: If n is an even integer, then it is divisible by 2.
- **Converse**: If n is divisible by 2, then n is an even integer.
- **Contrapositive**: If n is not divisible by 2, then n is not an even integer.