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1.Relation and Function
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If $A = \left\{ {1,2,3,......m} \right\},$ then total number of reflexive relations that can be defined from $A \to A$ is
A
${2^{{m^2} - m}}$
B
${2^{{m^2}}}$
C
${2^{{m^2} - m+1}}$
D
${2^{{m^2} + m}}$
Solution
$\because n(A \times A)=m^{2}$
$\therefore$ Any reflexive relation must have $(1,1)$
$(2,2) \dots(m, m)$ i.e. $m$ elements and may contain any mumber of elements out of rest $\left(m^{2}-m\right)$
$\Rightarrow \mathrm{m}^{2}-\mathrm{m} \mathrm{C}_{0}+^{\mathrm{m}^{2}-\mathrm{m}} \mathrm{C}_{1}+\ldots+\mathrm{t}^{\mathrm{m}^{2}-\mathrm{m}} \mathrm{C}_{\mathrm{m}^{2}-\mathrm{m}}=2^{\mathrm{m}^{2}-\mathrm{m}}$
are total number of reflexive rela tion
Standard 12
Mathematics
