Example-6.
Let A = {1, 2, 3, 4, 5}; B = {4, 5, 6, 7}. Find A – B.

Solution :
Given A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}. Only the elements which are in A but not in B should be taken.

A – B = {1, 2, 3, 4, 5} – {4, 5, 6, 7} = {1, 2, 3}

Therefore, A – B = {1, 2, 3}.
Since 4, 5 are the elements in B they are taken away from A.

Similarly for B – A, the elements which are only in B are taken.

B – A = {4, 5, 6, 7} – {1, 2, 3, 4, 5} = {6, 7}

Therefore, B – A = {6, 7} (4, 5 are the elements in A and so they are taken away from B).

Note that A – B not equal to B – A

The Venn diagram of A – B and B – A are shown below.


Do This

1. If A = {1, 2, 3, 4 ,5} and B = {4, 5, 6, 7}, then find A – B and B – A. Are they equal ?

2. If V = {a, e, i, o, u} and B = {a, i, k, u}, find V – B and B – V


Think And Discuss

The sets A – B, B – A and A ∩ B are mutually disjoint sets. Use examples to observe if this is true


EXERCISE - 2.2

1. If A = {1, 2, 3, 4} and B = {1, 2, 3, 5, 6}, then find A ∩ B and B ∩ A. Are they equal?

2. If A = {0, 2, 4}, find A ∩ ∅ and A ∩ A. Comment.



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