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Proof of Set Relationships Using Element Definitions

A proof of set relationships using element definitions in mathematical set theory.

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    Proof of Set Relationships Using Element Definitions Question: AN(BUC)=(ANB)U(ANC) Proof: To show that 4n(BUC)=(4nB)U(4NC), we prove in (1) that AN(BUC) (AN B)U(ANC), and in (2) that (4nB)U(ANC)c AN(BUC). (1) An(BUC)c(ANB)U(ANC) We take any element xe An (Bu). By the definition, we have that xed and xeBuUC. As xe BuC, we have that xeBor xeC. So, xe4 and xeB,0r xe4 and xeC. Namely, xe ANB or xe AnC. Hence, xe(ANB)U(ANC). So, AN(BUC)c(ANB)U(ANC).

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