Let A = {1, 2, 3}. Find the number of binary operations on A.

Explanation

To find the number of binary operations on the set \( A = \{1, 2, 3\} \), we can follow these steps:

### Step 1: Understand the Definition of a Binary Operation
A binary operation on a set \( A \) is a function that combines any two elements of \( A \) to form another element of \( A \). In mathematical terms, a binary operation \( * \) on a set \( A \) is a function \( *: A \times A \rightarrow A \).

### Step 2: Determine the Number of Elements in Set A
The set \( A \) has 3 elements: \( 1, 2, 3 \). Therefore, the number of elements \( n \) in set \( A \) is \( n = 3 \).

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