Let $$A = \left\{ {1,\,2,\,3} \right\}.$$ 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 :
$${2^9}$$
Solution :
$$n\left( {A \times A} \right) = n\left( A \right).n\left( A \right) = {3^2} = 9.$$ So, the total number of subsets of $${A \times A}$$ is $${2^9}$$ and a subset of $${A \times A}$$ is a relation over the set $$A.$$
Releted MCQ Question on Calculus >> Sets and Relations
Releted Question 1
If $$X$$ and $$Y$$ are two sets, then $$X \cap {\left( {X \cup Y} \right)^c}$$ equals.