Q2 of 162 Page 1

For any two sets A and B, prove the following:

A – B = A Δ (A ∩ B)

= A Δ (A ∩ B) [∵ E Δ F =(E–F) ∪ (F–E) ]


= (A–( A ∩ B)) ∪ (A ∩B –A) [∵ E – F = E ∩ F’]


= (A ∩ (A ∩ B)’) ∪ (A∩B∩A’)


= (A ∩ (A’∪B’)) ∪ (A∩A’∩B)


= ϕ ∪ (A ∩ B’) ∪ ϕ


= A ∩ B’ [∵A ∩ B’ = A–B]


= A–B


=LHS


∴ LHS=RHS Proved.


More from this chapter

All 162 →
2

For any two sets A and B, prove the following:

A – (A – B) = A ∩ B

 2

For any two sets A and B, prove the following:

A ∩ (A ∪ B’) = ϕ

 3

If A, B, C are three sets such that A ⊂ B, then prove that C – B ⊂ C – A.

 4

For any two sets A and B, prove that

(A ∪ B) – B = A – B