Sets And Relations Question 8
Question 8 - 2024 (30 Jan Shift 2)
The number of symmetric relations defined on the set ${1,2,3,4}$ which are not reflexive is
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Answer (960)
Solution
Total number of relation both symmetric and reflexive $=2^{\frac{n^{2}-n}{2}}$
Total number of symmetric relation $=2^{\left(\frac{n^{2}+n}{2}\right)}$
$\Rightarrow$ Then number of symmetric relation which are not reflexive
$\Rightarrow 2^{\frac{n(n+1)}{2}}-2^{\frac{n(n-1)}{2}}$
$\Rightarrow 2^{10}-2^{6}$
$\Rightarrow 1024-64$
$=960$
