Relations and Functions

Relations and Functions

Question

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

Answer
space space space space space space space space space space straight A apostrophe space minus space straight B apostrophe space equals space space straight A apostrophe space intersection space left parenthesis straight B apostrophe right parenthesis apostrophe                                               (By involution law)
            
          space space space space space space space space space space space space space space space space equals space straight A apostrophe space intersection space straight B

space space space space space space space space space space space space space space space space space space space equals space straight B space intersection space straight A apostrophe space equals space straight B minus straight A
Hence,     A' - B' = B - A
      

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