 Three Exercises Involving Sets

Subject Mathematics Abstract Algebra

Question

0.2) Given the sets: Z, S={2,5,√2,25,π,5/2} ; T={4,25, √2, 6, 3/2}, prove that:
Z ∩ (S U T) =(Z ∩ S) U (Z ∩ T) and Z U ( S ∩ T) = (Z U S) ∩ (Z U T).

0.3) Let T and S be sets. Prove that S ∩ (S U T) =S and S U (S ∩ T) = S.

0.5) Let A, B, and C be sets. Prove that A ∩ ( B U C) = (A ∩ B ) U ( A ∩ C).

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