Write the inverse of the given conditiona statement :
If a number n is even , then `n^(2)` is even .

Answer

To find the inverse of the given conditional statement, we will follow these steps:

### Step 1: Identify the Conditional Statement
The original conditional statement is:
"If a number \( n \) is even, then \( n^2 \) is even."

### Step 2: Define the Components
Let's define:
- \( p \): "A number \( n \) is even."
- \( q \): "\( n^2 \) is even."

The statement can be expressed as:
\( p \implies q \)

### Step 3: Write the Inverse
The inverse of a conditional statement \( p \implies q \) is given by:
\( \neg p \implies \neg q \)

Where:
- \( \neg p \): "A number \( n \) is not even."
- \( \neg q \): "\( n^2 \) is not even."

### Step 4: Rewrite the Inverse Statement
Now, we can rewrite the inverse statement using the definitions:
"If a number \( n \) is not even, then \( n^2 \) is not even."

### Step 5: Simplify the Terms
The term "not even" can be simplified to "odd," since the opposite of even is odd. Therefore, we can rewrite the statement as:
"If a number \( n \) is odd, then \( n^2 \) is odd."

### Final Answer
The inverse of the statement "If a number \( n \) is even, then \( n^2 \) is even" is:
"If a number \( n \) is odd, then \( n^2 \) is odd."

---