Given that P = {x : 2 ≤ x ≤ 8} and Q = {x : 4 < x ≤ 12} are subsets of the universal set μ = {x : x ∈ R}, find (P ⋂ Q\(^1\)).
- {x : 4 < x < 8}
- {x : 2 < x ≤ 4}
-
{x : 2 ≤ x ≤ 4}
- {x : 4 ≤ x ≤ 8}
The correct answer is: C
Explanation
P = {x : 2 ≤ x ≤ 8} = {2, 3, 4, 5, 6, 7, 8}
Q = {x : 4 < x ≤ 12} = {5, 6, 7, 8, 9, 10, 11, 12}
Q1 = R - {5, 6, 7, 8, 9, 10, 11, 12} = {..., 2, 3, 4, 13, 14, 15, ...}
∴ P ⋂ Q\(^1\) = {2, 3, 4} = {x : 2 ≤ x ≤ 4}