Q6 of 145 Page 33

Given an example of three sets A, B, C such that A ∩ C ≠ ϕ, B ∩ C ≠ ϕ, A ∩ C ≠ ϕ, and A ∩ B ∩ C = ϕ

Let A = {1, 2}


B = {2, 3}


C = {1, 3, 4}


AB = {2}


AC = {1}


BC = {3}


ABC = {2} {1, 3, 4} = ø


So the three sets are valid and satisfy the given conditions


More from this chapter

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4

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}, and = {2, 3, 5, 7} verify that:

(i) (A ∪ B)’ = (A’ ∩ B’)


(ii) (A ∩ C)’ = (A’ ∪ B’)


 5

Let A = {a, b, c}, B = {b, c, d, e} and = {c, d, e, f} be subsets of U = {a, b, c, d, e, f}. Then verify that:

(i) (A’)’ = A


(ii) (A ∪ B)’ = (A’ ∩ B’)


(iii) (A ∩ B)’ = (A’ ∪ B’)


 7

For any sets A and B, prove that:

(i) (A – B) ∩ B = ϕ


(ii) A ∪ (B – A) = A ∪ B


(iii) (A – B) ∪ (A ∩ B) = A


(iv) (A ∪ B) – B = A – B


(iv) A – (A ∪ B) = A – B


 8

For any sets A and B, prove that:

(i) A ∩ B’ = ϕ ⇒ A B


(ii) A’ ∪ B’ = U ⇒ A B