# Sets Questions

## Let A and B be two sets containing 2 elements and 4 elements, respectively. The number of subsets A$$\times$$B having 3 or more elements is

Solution : Given, n(A) = 2 and n(B) = 4 $$\therefore$$ n(A$$\times$$B) = 8 The number of subsets of (A$$times$$B) having 3 or more elements = $$^8C_3 + {^8C_4} + ….. + {^8C_8}$$ = $$2^8 – {^8C_0} – {^8C_1} – {^8C_2}$$ = 256 – 1 – 8 – 28 = 219     [$$\because$$ $$2^n$$ = …

## 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}} Similar Questions Let A and B be two sets containing 2 elements and 4 elements, respectively. The number of subsets A$$\times$$B having 3 or more elements is If aN = {ax : x $$\in$$ …

## 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 Similar Questions If A = {x,y}, then the power set of A is If A = {2, 4} and B = {3, 4, 5} then (A $$\cap$$ B) …

## 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 …

## 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 = $$\phi$$ Similar Questions If A = {x,y}, then the power set of A is If aN = {ax : x $$\in$$ N}, then the …

## If N is a set of first 10 natural numbers and a relation R is defined as a + 2b = 10 where a, b $$\in$$ N. find inverse of R.

Solution : R = {(2, 4), (4, 3), (6, 2), (8, 1)} $$R^{-1}$$ = {(4, 2), (3, 4), (2, 6), (1, 8)} Similar Questions If A = {x,y}, then the power set of A is If aN = {ax : x $$\in$$ N}, then the set 6N $$\cap$$ 8N is equal to Let A = …

## If A = {2, 4} and B = {3, 4, 5} then (A $$\cap$$ B) $$\times$$ (A $$\cup$$ B)

Solution : (A $$\cap$$ B) = {4} and (A $$\cup$$ B) = {2, 3, 4, 5} $$\therefore$$ (A $$\cap$$ B) $$\times$$ (A $$\cup$$ B) = {(4, 2), (4, 3), (4, 4), (4, 5)} Similar Questions If A = {x,y}, then the power set of A is If aN = {ax : x $$\in$$ N}, then …