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Zeal Test Series 2019: Set Theory & Algebra  Relations
0
votes
67
views
The Number of Relations, Which are both Reflexive and Symmetric but not AntiSymmetric, on a
set with 6 elements, are ____________?
i got 32768 plz check
zeal
discretemathematics
settheory&algebra
relations
zeal2019
asked
Jan 2
in
Set Theory & Algebra
by
Prince Sindhiya
Loyal
(
5.4k
points)
recategorized
Mar 6
by
ajaysoni1924

67
views
answer
comment
0
What is the answer? 245760?
0
yes I also got 32768
0
answer given 32767
0
$2^{\frac{n^{2} n}{2}}$ 1
it also take a condition in which we didn't choose any of the element which is not in a diagonal
0
@MAGMA MEANS {(1,1)......(6,6)} WHICH IS SYMMETRIC, REFLEXIVE and ANTISYMMETRIC So we have to subtract these case Right?
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2
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+1
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since it is reflexive as well as symmetric. therefore, all self pairs will definitely be there. and no. of symmetric relations = 2^((n^2n)/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..
answered
Mar 13
by
karan25gupta
(
195
points)
edited
Mar 13
by
karan25gupta
comment
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+1
vote
i am getting 32767.
answered
Mar 13
by
abhishekmehta4u
Boss
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33.9k
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