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Problem 7: Show that for any sets A, B, C there is a bijection between A and (A^C).Problem: Recall the relation composition operator defined as:Ri; Rz = (a,c) | there exists b with (a, b) ∈ Rz and (b, c) ∈ RiLet S be an arbitrary set. For each of the following, prove that it holds for any binary relations Ri, Rz, and Ra, or give a counterexample to disprove:(Ri; Rz); Ra = Ri; (Rz; Ra) (4 marks)I;R1 = Rc; / = Ri where / = (x,x) : x ∈ S (4 marks)(Ri U Re); Ra = (Ri; R) U (Rz; Ro) (4 marks)Ri
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