Prove that A-B' = AnB if A and B are any two sets.
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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∈
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B
\implies x\in A⟹x∈A and x\in B'x∈B
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\implies x\in A\cap B'⟹x∈A∩B
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\implies A-B=A\cap B'⟹A−B=A∩B
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similarly, Let y is an arbitrary element of A\cap B'A∩B
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then, y\in A\cap B'y∈A∩B
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\implies y\in A⟹y∈A and y\in B'y∈B
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\implies y\in A⟹y∈A and y\notin By∈
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B
\implies y\in A-B⟹y∈A−B
\implies A\cap B'=A-B⟹A∩B
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=A−B
hence proved//
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