Question

Which of the following has no solution?

(x + 1 < -1) ∩ (x + 1 < 1)
(x + 1 ≤ 1) ∩ (x + 1 ≥ 1)
(x + 1 < 1) ∩ (x + 1 > 1)

Answer 1

(x + 1 < 1) ∩ (x + 1 > 1)

Explanation:

Answer 2

(x + 1 < 1) ∩ (x + 1 > 1)

Explanation:

By subtracting 1 from both sides of each of the inequalities, the sets of inequalities resolve to ...

1. x < -2 ∩ x < 0 . . . . solution: x < -2

2. x ≤ 0 ∩ x ≥ 0 . . . . solution: x = 0

3. x < 0 ∩ x > 0 . . . . no solution

The third set of inequalities has no solution.