# Sets Examples

Here you will learn some sets examples for better understanding of sets concepts.

Example 1 : The set A = [x : x $$\in$$ R, x^2 = 16 and 2x = 6] equal-

Solution : $$x^2$$ = 16 $$\implies$$ x = $$\pm$$4

2x = 6 $$\implies$$ x = 3

There is no value of x which satisfies both the above equations.

Thus, A = $$\phi$$

Example 2 : Let A = [x: x $$\in$$ R, |x| < 1]; B = [x : x $$\in$$ R, |x – 1| $$\ge$$ 1] and A $$\cup$$ B = R – D, then the set D is-

Solution : A = [x: x $$\in$$ R,-1 < x < 1]

B = [x : x $$\in$$ R, x – 1 $$\le$$ -1 or x – 1 $$\ge$$ 1]

[x: x $$\in$$ R, x $$\le$$ 0 or x $$\ge$$ 2]

$$\therefore$$ A $$\cup$$ B = R – D

where D = [x : x $$\in$$ R, 1 $$\le$$ x < 2]

Example 3 : If aN = {ax : x $$\in$$ N}, then the set 6N $$\cap$$ 8N is equal to-

Solution : 6N = {6, 12, 18, 24, 30, …..}

8N = {8, 16, 24, 32, ….}

$$\therefore$$ 6N $$\cap$$ 8N = {24, 48, …..} = 24N

Example 4 : If A = {x,y}, then the power set of A is-

Solution : Clearly P(A) = Power set of A

= set of all subsets of A

= {$$\phi$$, {x}, {y}, {x,y}}

Practice these given sets examples to test your knowledge on concepts of sets.