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Solution


Q.

The number of symmetric relations defined on the set {1, 2, 3, 4} which are not reflexive is _______.    [2024]

Ans.

(960)

Let A = {1, 2, 3, 4}

∴n(A)=4

∴  Number of reflexive and symmetric relation =2n2-n2=26

Number of symmetric relations =2n(n+1)2=210

∴ Number of relations which is symmetric but not reflexive =210-26=1024-64=960