Zeal Test Series 2019: Set Theory & Algebra - Relations

Question

The Number of Relations, Which are both Reflexive and Symmetric but not Anti-Symmetric, on a

set with 6 elements, are ____________?

i got 32768 plz check

Comments

answer given 32767

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$2^{\frac{n^{2} -n}{2}}$  -1

it also take a condition in which we didn't choose any of the element which is not in a diagonal

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@MAGMA MEANS {(1,1)......(6,6)} WHICH IS SYMMETRIC, REFLEXIVE and ANTISYMMETRIC So we have to subtract these case Right?

Answer 1

i am getting 32767.

Answer 2

since it is reflexive as well as symmetric. therefore, all self pairs will definitely be there. and no. of symmetric relations = 2^((n^2-n)/2)

hence it is 2^15 i.e. 32768 but we will have to subtract one case when only self pairs will appear in relation. because relation with only self pairs is symmetric as well as antisymmetric..