Consider set A = {1,2,3} . Number of symmetric relations that can be defined on A containing ordered

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1.Relation and Function

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Consider set $A = \{1,2,3\}$ . Number of symmetric relations that can be defined on $A$ containing the ordered pair $(1,2)$ & $(2,1)$ is

A

$18$

B

$16$

C

$24$

D

$32$

Solution

$\mathrm{n}(\mathrm{A} \times \mathrm{A})=9$

Relation containing $(1,2),(2,1),(a, a)=2^{3}$

Relation containing

$(1,2),(2,1),(1,3),(3,1),(\mathrm{a}, \mathrm{a})=2^{3}$

Relation containing

$(1,2),(2,1),(2,3),(3,2),(\mathrm{a}, \mathrm{a})=2^{3}$

Relation containing

$(1,2),(2,1),(1,3),(3,1),(2,3),(3,1)(a, a)=2^{3}$

$\Rightarrow$ Total number of relation $=32.$

Standard 12

Mathematics

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