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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
recategorized by | 119 views
What is the answer? 245760?
yes I also got  32768
answer given 32767
$2^{\frac{n^{2} -n}{2}}$  -1

it also take a condition in which we didn't choose any of the element which is not in a diagonal
@MAGMA MEANS {(1,1)......(6,6)} WHICH IS SYMMETRIC, REFLEXIVE and ANTISYMMETRIC So we have to subtract these case Right?

2 Answers

+2 votes

i am getting 32767.

by Boss
+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..
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