Question

prove that a minus b union c equals to a minus b intersection a minus C

Answer 1

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Answer 2

Given:

Two Sets are given i.e.  A, B, C

To Find:

A-(B∪C)=(A-B)∩(A-C)

Solution:

A-(B∪C)=(A-B)∩(A-C)

Taking left hand side first,

L.H.S.

      =A-(B∪C)

     =A∩(B∪C)'

     =A∩(B'∩C')  ( De Morgans's Law)

     =(A∩B')∩(A∩C')

     =(A∪B)∩(A∪C)...............................(1)

R.H.S.

         (A-B)∩(A-C)

        =(A∪B')∩(A∩C')

        =(A∪B)∩(A∪C).................(2)

From eq1 and eq2, we get L.H.S=R.H.S.

Hence A-(B∪C)=(A-B)∩(A-C)