Q. 215.0( 2 Votes )

# Using properties of sets prove the statements givenFor all sets A and B, (A ∪ B) – B = A – B

Given: There are two sets A and B

To prove: (A B) – B = A – B

Take L.H.S

(A B) – B

= (A B) B’

{ A – B = A B’}

= (A B’) (B B’)

{ Distributive property of set:

(A B) (A C) = A (B C)}

= (A B’) Φ

{ A A’ = Φ}

= A B’

= A – B

{ A – B = A B’}

= R.H.S

Hence Proved

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RS Aggarwal - Mathematics