Q8 of 145 Page 33

For any sets A and B, prove that:

(i) A ∩ B’ = ϕ ⇒ A B


(ii) A’ ∪ B’ = U ⇒ A B


(i) The Venn Diagram for the given condition is given below



As can be seen from the Venn Diagram, A is a proper subset of B


AB


(ii) Wrong question. If A is a proper subset of B then A’B’≠U



More from this chapter

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6

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

 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


 1

Let A = {a, b, c, e, f} B = {c, d, e, g} and C = {b, c, f, g} be subsets of the set U = {a, b, c, d, e, f, g, h}.

(i) A ∩ B


(ii) A ∪ (B ∩ C)


(iii) A – B


(iv) B – A


(v) A – (B ∩ C)


(vi) (B – C) ∪ (C – B)


 2

Let A = {2, 4, 6, 8, 10}, B = {4, 8, 12, 16} and C = {6, 12, 18, 24}.

Using Venn diagrams, verify that:


(i) (A ∪ B) ∪ C = A ∪ (B ∪ C)


(ii) (A ∩ B) ∩ C = A ∩ (B ∩ C).