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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
