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Prove that A-B' = AnB if A and B are any two sets. |
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Answer» Answer: A- B means EVERYTHING in A except for anything in A\cap BA∩B Let X is an arbitrary ELEMENT of A - B it means , X\in A-BX∈A−B \implies x\in A⟹x∈A and x\notin Bx∈ / B \implies x\in A⟹x∈A and x\in B'x∈B ′
\implies x\in A\cap B'⟹x∈A∩B ′
\implies A-B=A\cap B'⟹A−B=A∩B ′
SIMILARLY, Let y is an arbitrary element of A\cap B'A∩B ′
then, y\in A\cap B'y∈A∩B ′
\implies y\in A⟹y∈A and y\in B'y∈B ′
\implies y\in A⟹y∈A and y\notin By∈ / B \implies y\in A-B⟹y∈A−B \implies A\cap B'=A-B⟹A∩B ′ =A−B hence proved// |
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