Question 1
Sets and LogicIf P = {x : 1 ≤ x ≤ 6} and Q = {x : 2 < x < 9}, where x ∈ R, find P ∩ Q.
- A.{x : 2 ≤ x ≤ 6}
- B.{x : 2 ≤ x < 6}
- C.{x : 2 < x < 6}
- D.{x : 2 < x ≤ 6}
Show the answer and explanation
Answer: D ({x : 2 < x ≤ 6})
Explanation
The intersection keeps the numbers in both sets: they must be greater than 2 (from Q) and at most 6 (from P), so P ∩ Q = {x : 2 < x ≤ 6}.