The number of commutative binary operations that can be defined on a set of `2` elements is

Options

A. `1`
B. `2`
C. `4`
D. `16`

Explanation

To find the number of commutative binary operations that can be defined on a set with 2 elements, we can follow these steps:

### Step 1: Understand the formula for commutative binary operations
The formula for the number of commutative binary operations on a set with \( n \) elements is given by:
\[ n^{n^{n-1}/2} \]

### Step 2: Substitute the value of \( n \)
In our case, we have a set with \( n = 2 \) elements. Therefore, we substitute \( n \) in the formula:
\[ 2^{2^{2-1}/2} \]

### Step 3: Simplify the exponent
Now, simplify the exponent:
\[ 2^{2^{1}/2} = 2^{2^{1}/2} = 2^{2/2} = 2^{1} \]

### Step 4: Calculate the final result
Now, calculate \( 2^{1} \):
\[ 2^{1} = 2 \]

### Conclusion
Thus, the number of commutative binary operations that can be defined on a set of 2 elements is \( 2 \).