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