(a) Here, E₁ = multiples of `3`:

E₁ = {3, 6, 9,12, 15, 18, 21}

n(E₁) = 7

E₂ = multiples of `8`:

E₂ = {8, 16}

n(E₂) = 2

Events E₁ and E₂ are mutually exclusive.

n(E) = n(E₁) + n(E₂) = 7 + 2 = 9

(b) Here, E₁ = multiples of `2`:

E₁ = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}

n(E₁) = 11

E₂ = multiples of `3`:

E₂ = {3, 6, 9,12, 15, 18, 21}

n(E₂) = 7

Events E₁ and E₂ are not mutually exclusive.

We could proceed as follows:

n(E) = n(E₁) + n(E₂) - n(E₁ ∩ E₂) = 11 + 7 − 3 = 15

where E₁ ∩ E₂ means "the intersection of the sets E₁ and E₂".