Part (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

Part (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(E1E2) = 11 + 7 − 3 = 15

where E1E2 means "the intersection of the sets E1 and E2".