Question

If P = {x : 3x + 4 ≤ 23, x ∈ N} and Q = {x : −6 ≤ 2x + 2 < 9, x ∈ I} find PQ.

Answer 1

PQ = P ∩ Q

Find set P

P = {x : 3x + 4 ≤ 23, x ∈ N}

3x ≤ 19

`x <=  19/3`

= 6.33

Since x ∈ N = {1, 2, 3, …},

P = {1, 2, 3, 4, 5, 6}

Find set Q

Q = {x : −6 ≤ 2x + 2 < 9, x ∈ I}

−6 ≤ 2x + 2 < 9

−8 ≤ 2x < 7

−4 ≤ x < 3.5

Q = {−4, −3, −2, −1, 0, 1, 2, 3}

Find PQ = P ∩ Q

P = {1, 2, 3, 4, 5, 6}

Q = {−4, −3, −2, −1, 0, 1, 2, 3}

PQ = {1, 2, 3}​