Question

Find the cardinal number of the following sets:

A₄ = {b : b ∈ Z and –7 < 3b – 1 ≤ 2}

Answer 1

A₄ = {b : b ∈ Z and –7 < 3b –1 ≤ 2}

–7 < 3b – 1

⇒ –7+1 < 3b –1+1
(Adding 1 to both sides)

⇒ –6 < 3b

⇒ `-(6)/(3)` < b
(Dividing both sides by 3)

⇒ –2 < b

Again 3b – 1 ≤ 2

⇒ 3b –1 + 1 ≤ 2 + 1 (Adding 1 to both sides)

⇒ 3b ≤ 3

⇒ b ≤ `(3)/(3)`
(Dividing both sides by 3)

⇒ b ≤ 1

∴  –2 ≤ b ≤ 1

∴ Given set A₄ = {–1, 0, 1}

∴  Cardinal number of set A₄ = 3