Question

Let \( A = \{1, 2, 3\} \). Which of the following is the number of distinct relations on \( A \)?

• A. 256
• B. 158
• C. 512
• D. 1024

Hint:

To find the number of distinct relations on a set, use the formula $2^{n^2}$, where $n$ is the number of elements in the set.

Answer 1

The Correct Option is C

The number of distinct relations on a set $A$ is given by $2^{n^2}$, where $n$ is the number of elements in the set. Here, $A = \{1, 2, 3\}$, so $n = 3$. 
Thus, the number of relations is: \[ \text{Number of relations} = 2^{n^2} = 2^{3^2} = 2^9 = 512 \]