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

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2.Relations and Functions

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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

Solution

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

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 $A$.

Standard 11

Mathematics

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