Number of symmetric relations defined on set {1,2,3,4} which are not reflexive is

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1.Relation and Function

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The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is

A

$950$

B

$940$

C

$960$

D

$965$

(JEE MAIN-2024)

Solution

Total number of relation both symmetric and reflexive $=2^{\frac{\mathrm{n}^2-\mathrm{n}}{2}}$

Total number of symmetric relation $=2^{\left(\frac{\mathrm{n}^2+\mathrm{n}}{2}\right)}$

$\Rightarrow$ Then number of symmetric relation which are not reflexive

$ \Rightarrow $ $ 2^{\frac{n(n+1)}{2}}-2^{\frac{n(n-1)}{2}}$

$ \Rightarrow $ $2^{10}-2^6 $

$\Rightarrow $ $1024-64 $

$ =960$

Standard 12

Mathematics

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