Question

Choose the correct answer:

1. Let A = {x ∈ R : | x + 1 | < 2} and B = {x ∈ R : | x – 1| ≥ 2}. Then which one of the following statements is NOT true?

• A. A – B =(–1, 1)
• B. B – A = R – (–3, 1)
• C. A ⋂ B = (–3, –1]
• D. A U B = R – [1, 3)

Answer 1

Answer: (A)

A – B =(–1, 1)

Answer 2

The correct option is(B): B – A = R – (–3, 1).

A = (–3, 1) and B = (–∞, –1] ∪ [3, ∞)

So, A – B = (–1, 1)

B – A = (–∞, –3] ∪ [3, ∞) = R – (–3, 3)

A ∩ B = (–3, –1]

and A ∪ B = (–∞, 1) ∪ [3, ∞) = R – [1, 3)