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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
in Set Theory & Algebra by Loyal (5.4k points)
recategorized by | 74 views
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What is the answer? 245760?
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yes I also got  32768
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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?

2 Answers

+1 vote
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..
by (239 points)
edited by
+1 vote

i am getting 32767.

by Boss (34.4k points)

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