Q7 of 162 Page 1

For any two sets, prove that:

A ∪ (A ∩ B) = A

A ∪ (A ∩ B) [∵ union is distributive over intersection]


(A ∪ A) ∩ (A ∪ B)[∵ A ∪ A = A]


= A ∩ (A ∪ B)


= A.


More from this chapter

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6

For three sets A, B, and C, show that

A ∩ B = A ∩ C need not imply B = C.

 6

For three sets A, B, and C, show that

A ⊂ B C – B ⊂ C – A

 7

For any two sets, prove that:

A ∩ (A ∪ B) = A

 8

Find sets A, B, and C such that A ∩ B, A ∩ C and B ∩ C are non–empty sets and A ∩ B ∩ C = ϕ.