[Figs . (i) to (v)]. A B U Fig . (iii) (iv) (v) Figs .
(i) to (v) SETS Fig . Fig . . .
Difference of sets The difference of the sets A and B in this order is the set of elements which belong to A but not to B. Symbolically, we write A – B and read as “ A minus B”. Example Let A = { , , , , , }, B = { , , , }. Find A – B and B – A.
Solution We have, A – B = { , , }, since the elements , , belong to A but not to B and B – A = { }, since the element belongs to B and not to A. We note that A – B ≠ B – A. Example Let V = { a, e, i, o, u } and B = { a, i, k, u }. Find V – B and B – V Solution We have, V – B = { e, o }, since the elements e, o belong to V but not to B and B – V = { k }, since the element k belongs to B but not to V.
We note that V – B ≠ B – V. Using the set- builder notation, we can rewrite the definition of difference as A – B = { x : x ∈ A and x ∉ B } The difference of two sets A and B can be represented by Venn diagram as shown in Fig . . The shaded portion represents the difference of the two sets A and B.
Remark The sets A – B, A ∩ B and B – A are mutually disjoint sets, i.e., the intersection of any of these two sets is the null set as shown in Fig . . EXERCISE . .
Find the union of each of the following pairs of sets : X = { , , } Y = { , , } A =