show A intersect B union AC ACBSolutionI Will show this by c

show (A intersect B) union (A-C)= A-(C-B)

Solution

I Will show this by counter example

let A={1,2,3,4}, B={4,5,6,7,8}

    C={1,2,3,4,5,6,7,8}

now L.H.S=(AB)(A-C)

first (AB)={4}
now (A-C)={ }

then (AB)(A-C)={4}------->1

R.H.S=A-(C-B)

first C-B={1,2,3}

now A-(C-B)={1,2,3,4}-{1,2,3}

                 ={4}------>2

From equations 1 and 2

L.H.S=R.H.S

i.e(AB)(A-C)=A-(C-B)