Relations and Functions

Relations and Functions

Question

Show that :

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

Answer

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

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


 
   

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