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Question
For any two sets A and B, prove that :
\[A' - B' = B - A\]
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Solution
\[LHS = A' - B'\]
\[ = A' \cap \left( B' \right)' \left[ \because C - D = C \cap D' \right]\]
\[ = A' \cap B\]
\[ = B \cap A'\]
\[ = B - A \left[ \because C \cap D' = C - D \right]\]
\[RHS = B - A\]
So, LHS = RHS
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