### Group theory, cardinality and isomorphic example problems

I would like to know how to identify and prove the cardinality of sets and how to identify isomorphic. (See attached file for full problem description) Group Theory: a. If S and T are sets then let TS denote the set of all functions from S to T. Prove that the cardinality of TSxU equals the cardinality of (TS)U b. C