Question

Given U = {10, 11, 12, 13, 14, ... , 20}, A = {10, 12, 14, 16, 18} and B = {10, 11, 12, 13, 14, 15},
1. (AnB)' = A'uB'​

Answer 1

The difference of two subsets A and B is a subset of U, denoted by A – B and is defined by

A – B = {x : x ∈ A and x ∉ B}.

Let A and B be two sets. The difference of A and B, written as A - B, is the set of all those elements of A which do not belongs to B.

Thus A – B = {x : x ∈ A and x ∉ B} or A – B = {x ∈ A : x ∉ B}.

Clearly, x ∈ A – B

⇒ x ∈ A and x ∉ B

In the adjoining figure the shaded part represents A – B.

Difference of Sets using Venn Diagram

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Similarly, the difference B – A is the set of all those elements of B that do not belongs to A.

Thus, B – A = {x : x ∈ A and x ∉ B} or A – B = {x ∈ B : x ∉ A}.