Sets Examples

SETS EXAMPLES

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}}


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