Question

Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A is

• A. $2 ^ { 9 }$
• B. 6
• C. 8
• D. None of these

Answer 1

Answer: (A)

$2 ^ { 9 }$

Answer 2

$n ( A \times A ) = n ( A ) \cdot n ( A ) = 3 ^ { 2 } = 9$

So, the total number of subsets of $2 ^ { 9 }$ and a subset of $A \times A$ is a relation over the set A.