Question

for any two sets A and B prove that B'-A'=A-B​

Answer 1

Answer:

A - B means everything in A except for anything in A\cap B

Let X is an arbitrary element of A - B

it means , X\in A-B

\implies x\in A and x\notin B

\implies x\in A and x\in B'

\implies x\in A\cap B'

\implies A-B=A\cap B'

similarly, Let y is an arbitrary element of A\cap B'

then, y\in A\cap B'

\implies y\in A and y\in B'

\implies y\in A and y\notin B

\implies y\in A-B

\implies A\cap B'=A-B

hence proved//

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