For a set A, we define = {x | 3y A.{x} C y}. (a) Prove...

 

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For a set A, we define Â= {x | 3y € A.{x} C y}. (a) Prove that P(A) = A. (b) True or False? If A C B then A C B. (If True, give a proof, if False, give a concrete counterexample.) (c) Show by giving an example that A = B does not imply A = B. For a set A, we define Â= {x | 3y € A.{x} C y}. (a) Prove that P(A) = A. (b) True or False? If A C B then A C B. (If True, give a proof, if False, give a concrete counterexample.) (c) Show by giving an example that A = B does not imply A = B.

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