Question

The number of binary relations on a set with 3 elements is

• A. 8
• B. 16
• C. 512
• D. 128

Hint:

The number of binary relations on a set of \(n\) elements is \( 2^{n^2} \), as each pair of elements can either have a relation or not.

Answer 1

The Correct Option is C

The number of binary relations on a set with \(n\) elements is given by \( 2^{n^2} \). For a set with 3 elements, the calculation is: \[ 2^{3^2} = 2^9 = 512 \]
Therefore, the correct answer is 3. 512.