Question: 3. (25 points) Let S be a set with cardinality |S| = m and T be a set with cardinality |T| = n. Write a

3. (25 points) Let S be a set with cardinality |S| = m and T be a set with cardinality |T| = n. Write a formula for each of the following (assume that all functions mentioned are total functions): (a) The number of subsets of S with cardinality k.

(b) The number of functions from S to T.

(d) The number of onto (surjective) functions from S to T. (You may assume that m n.)

(e) The number of binary relations from S to T.

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