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Let s be a set with n elements and let a and b be distinct

Question: Let S be a set with n elements and let a and b be distinct elements of S. How many relations R are there on S such that

a) (a, b) ∈ R?

b) (a, b) ∈ R?

c) no ordered pair in R has a as its first element or b as its second element?

d) at least one ordered pair in R either has a as its first element or has b as its second element?

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Mathematics: Let s be a set with n elements and let a and b be distinct

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