Question

For all sets A and B, A – (A – B) = A ∩ B. Prove the statement.

Answer 1

let  A= {1,2,3}   and  B={1,2,3,4,5} 
L.H.S:
A-(A-B) = A-{ } = (1,2,3}
L.H.S = {1,2,3}
R.H.S:
A  INTERSECTION B 
= {1,2,3} INTERSECTION {1,2,3,4,5} = {1,2,3}
THEREFORE L.H.S = R.H.S
HENCE PROVED.