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.