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