For any two sets A and B, prove that (A' $-$ B') = (B $-$ A).

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Solution

$To prove : (A' - B') = (B - A) Proof : Let x \in (A' - B') \Rightarrow x \in A' & x \notin B' \Rightarrow x \notin A & x \in B \Rightarrow x \in (B - A) \Rightarrow (A' - B') \subseteq (B - A) . . . (i) Now, let x \in (B - A) \Rightarrow x \in B & x \notin A \Rightarrow x \notin B' & x \in A' \Rightarrow x \in (A' - B') \Rightarrow (B - A) \subseteq (A' - B') . . . (ii) Hence, from (i) and (ii), we have : (A' - B') = (B - A)$

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