Is * defined by `a`*`b=(a+b)/2` is binary operation on Z.

Explanation

To determine whether the operation defined by \( a * b = \frac{a + b}{2} \) is a binary operation on the set of integers \( \mathbb{Z} \), we need to verify if the result of this operation is also an integer whenever \( a \) and \( b \) are integers.

### Step-by-Step Solution:

1. **Definition of Binary Operation**:
A binary operation on a set is a function that takes two elements from the set and produces another element from the same set. In this case, we need to check if \( a * b \) results in an integer when \( a \) and \( b \) are integers.

2. **Operation Definition**:
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