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How many relations are there on a set with n elements that are: a) symmetric? b) antisymmetric? c) asymmetric? d) irreflexive? e) reflexive and symmetric?

How many relations are there on a set with n elements that are:

a) symmetric?

b) antisymmetric?

c) asymmetric?

d) irreflexive?

e) reflexive and symmetric?

f) neither reflexive nor irreflexive?

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