Define an associative binary operation on a set.

Explanation

To define an associative binary operation on a set, we can follow these steps:

### Step-by-Step Solution:

1. **Define a Set**: Let \( S \) be a non-empty set. For example, let \( S = \{1, 2, 3\} \).

2. **Define a Binary Operation**: A binary operation \( * \) on set \( S \) is a function that combines any two elements \( a, b \in S \) to produce another element \( c \in S \). For instance, we can define the operation \( * \) such that:
- \( 1 * 1 = 1 \)
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