Question

P is the solution set of 8x - 1 > 5x + 2 and Q is the solution set of 7x - 2 ≥ 3 (x + 6), where x є N. Find the set P ∩ Q.​

Answer 1

Answer:

P = { X : 7X – 2 > 4X + 1, X ∈ R }

7x – 2 > 4x + 1 7x – 4x > 1 + 2 3x > 3 X > 1

and

Q = {x: 9x – 45 ≥ 5 (x – 5)

, x ∈ R} 9x – 45 ≥

5x – 25 9x – 5x ≥ − 25 + 45 4x ≥ 20 X ≥ 5

(i) P ∩ Q = {x : x ≥ 5, x ∈ R}

(ii) P – Q = { X : 1 < X < 5, X ∈ R} (iii) P ∩ Q’ = {x : 1 < x < 5, x ∈ R}