Question

A solution set of 7x − 1 > 4x + 3 and B is the solution set of 5x – 1 ≥ 2 (x + 4) where x ∈ W, find A ∩ B.

Answer 1

W denotes the set of whole numbers (0, 1, 2, ...).

Solve A:

7x − 1 > 4x + 3

⇒ 3x > 4

`=> x > 4/3` With x ∈ W

A = {2, 3, 4, 5, ...}

Solve B:

5x − 1 ≥ 2(x + 4)

⇒ 5x − 1 ≥ 2x + 8

⇒ 3x ≥ 9

⇒ x ≥ 3 With x ∈ W

B = {3, 4, 5, ...}

Therefore A ∩ B = {3, 4, 5, ...}

= {x ∈ W | x ≥ 3}