If x ∈ I, A is the solution set of 2(x - 1) < 3x - 1 and B is the solution set of 4x – 3 ≤ 8 + x, find A ∩ B.

Given,

$2 (x - 1) \lt 3 x - 1 \\[0.5em] \Rightarrow 2x - 2 \lt 3x - 1 \\[0.5em] \Rightarrow 2x - 3x \lt - 1 + 2 \\[0.5em] \Rightarrow - x \lt 1 \\[0.5em] \Rightarrow x \gt - 1 \\[0.5em] \therefore \text{A} = \lbrace 0, 1, 2, 3, ….\rbrace$

Also,

$4x - 3 \le 8 + x \\[0.5em] \Rightarrow 4x - x \le 8 + 3 \\[0.5em] \Rightarrow 3x \le 11 \\[0.5em] \Rightarrow x \le \dfrac{11}{3} \\[0.5em] \therefore \text{B} = \lbrace….., -1, 0, 1, 2, 3\rbrace$

∴ A ∩ B = {0, 1, 2, 3}