Question

If P is the solution set of – 3x + 4 < 2x – 3, x ∈ N and Q is the solution set of 4x – 5 < 12, x ∈ W, find
(i) P ∩ Q
(ii) Q – P.

Answer 1

(i) – 3 x + 4 < 2 x – 3
– 3x – 2x < – 3 – 4 ⇒ – 5x < – 7

`-x < - (7)/(5) ⇒ x > (7)/(5)`
∴ Solution set P = {2, 3, 4, 5, .....}
(ii) 4x - 5 < 12
4x < 12 + 5 ⇒ 4x < 17

`x < (17)/(4)`
∴ Solution set Q = {4, 3, 2, 1, 0}
(i) P ∩ Q = {2, 3, 4}
(ii) Q - P = {1, 0}.