Question

If A = {x ∈ R: |x – 2| > 1}, B = {x∈R:√(x²-3>1)},C = {x∈R : |x - 4| ≥ 2} and Z is the set of all integers, then the number of subsets of the set (A ∩ B ∩ C)^C∩ Z is ___________.

Answer 1

A = (-∞,1)∪(3,∞)

B = (-∞,-2)∪(2,∞)

C = (-∞,2]∪[6,∞)

So,

A∩B∩C = (-∞,-2)∪[6,∞)

z∩(A∩B∩C)' = {-2,-1,0,-1,2,3,4,5}

Hence no. of its subsets = 2⁸ = 256