Question

If U ={x | x ∈ N , x < 10} and A = {x | x ∈ N , 2 ≤ x < 6} then (A′)′ is:

a) {1, 6, 7, 8, 9}
b) Power set{1, 2, 3, 4}
c) {2, 3, 4, 5}
d) { }
$\left[1\right]$

Answer 1

U ={x | x ∈ N , x < 10}= {1,2,3,4,5,6,7,8,9}
A= {x | x ∈ N , 2 ≤ x < 6}= {2, 3, 4, 5}

Then, A’= {1, 6, 7, 8, 9} [Since The Complement of a set A is the set of all elements of U that are not in A.]

$\therefore$ (A′)′= {2, 3, 4, 5} [The Complement of a set A’ is the set of all elements of U that are not in A’.]
Hence (A′)′= A= {2, 3, 4, 5}

Correct Option: c) {2, 3, 4, 5}