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

First finding solution set P

$-3 x + 4 \lt 2 x - 3 \\[0.5em] \Rightarrow - 3x - 2x \lt -3-4 \\[0.5em] \Rightarrow - 5x \lt - 7 \\[0.5em] \Rightarrow 5x \gt 7 \\[0.5em] \Rightarrow x \gt \dfrac{7}{5}$

∴ P = {2, 3, 4, 5, ….. }

Finding solution set Q

$\Rightarrow 4x-5 \lt 12 \\[0.5em] \Rightarrow 4x \lt 12 + 5 \\[0.5em] \Rightarrow 4x \lt 17 \\[0.5em] \Rightarrow x \lt \dfrac{17}{4}$

∴ Q = {4, 3, 2, 1, 0}

(i) P ∩ Q = {2, 3, 4}

(ii) Q – P = {0, 1}