Symmetric and anti-symmetric relation on a set, Mathematics

1. Let A = {1,2, 3,..., n}

(a) How many relations on A are both symmetric and anti-symmetric?

(b) If R is a relation on A that is anti-symmetric, what is the maximum number of ordered pairs that can be in R?

(c) How many anti-symmetric relations on A have the maximum size that you determined in part (b)?

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