Question

Find the cardinal number of the following sets:

A₃ = {p : p ∈ W and 2P - 3 < 8}

Answer 1

A₃ = {P : P ∈ W and 2P - 3 < 8}

2P - 2 < 8

⇒ 2P - 3 + 3 < 8 + 3
(Adding 3 to both sides)

⇒  2P < 11

⇒  P < ${\displaystyle \frac{11}{2}}$
(Dividing both sides by 2)

⇒  P < 5.5

∴ A₃ = {0, 1, 2, 3, 4, 5}

∴  Cardinal number of set A₃ = 6