Question

Consider U = {x|x is a real number}.

A = {x|x ∈ U and x + 2 > 10}
B = {x|x ∈ U and 2x > 10}

Which pair of statements is correct?

5 ∉ A; 5 ∈ B
6 ∈ A; 6 ∉ B
8 ∉ A; 8 ∈ B
9 ∈ A; 9 ∉ B

Answer 1

Solve the inequalities:

A: x + 2 > 10 ⇒ x > 8, so A = (8, ∞).
B: 2x > 10 ⇒ x > 5, so B = (5, ∞).

Check 8: 8 ∉ A (since 8 is not > 8) and 8 ∈ B (since 8 > 5).

Thus the correct pair is: 8 ∉ A; 8 ∈ B.