Q6 of 145 Page 36

Using Venn diagrams, show that (A – B), A ∩ B) and (B – A) are disjoint sets, taking A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12, 15, }.



A - B is denoted by the yellow region only


B - A is denoted by the blue region only


AB is denoted by the common region (blue +yellow)


There is no intersection between these three regions


Hence the three sets are disjoint sets.


More from this chapter

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4

Let A ⊂ B ⊂ U. Exhibit it in a Venn diagram.

 5

Let A = {2, 3, 5, 7, 11, 13}, B = {5, 7, 9, 11, 15} be subsets of U = {2, 3, 5, 7, 9, 11, 13, 15}.

Using Venn diagrams, verify that:


(i) (A ∪ B’) = (A’ ∩ B’)


(ii) (A ∩ B)’ = (A’ ∪ B’)


 1

If A and B are two sets such that n(A) = 37, n(B) = 26 and n (A ∪ B) = 51, find n (A ∩ B).

 2

If P and Q are two sets such that n(P ∪ Q) = 75, n (P ∩ Q) = 17 and n(P) = 49, find n (Q).