Relations and Functions

Relations and Functions

Question

Show that :

space space space space space space space straight A union left parenthesis straight B minus straight A right parenthesis space equals space straight A union straight B

Answer

L.H.S.   =   space space space space space space space space space space space straight A union left parenthesis straight B minus straight A right parenthesis equals straight A union left parenthesis straight B intersection straight A apostrophe right parenthesis
        space space space space space equals space left parenthesis straight A union straight B right parenthesis intersection left parenthesis straight A union straight A apostrophe right parenthesis                                                                      [By distribution law]
        space space space space space equals space left parenthesis straight A union straight B right parenthesis intersection left parenthesis straight A union straight A apostrophe right parenthesis                                                                 space space space space space space space space open square brackets because space straight A union straight A apostrophe equals straight U close square brackets
             = space space space space space space left parenthesis straight A union straight B right parenthesis intersection straight U                                                                    space space space space space space space space space space space open square brackets because space space straight A union straight U equals straight A close square brackets 
              = R.H.S.

∴   L.H.S. =R.H.S
Hence,  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space straight A union left parenthesis straight B minus straight A right parenthesis space equals space straight A union straight B

                                             

More Chapters from Relations and Functions