If a single card is drawn from a standard 52 card deck, in how many ways could it be a club or a jack?

13 ways for it to be a club

4 ways to be a jack

but wait .... the Jack of Clubs got counted both times!!!

we can't have that.

13 + 4 - 1 = 16

Or we could do it along the way

3 Jacks are not clubs

13 cards are clubs

3 + 13 = 16

Then general idea is:

count the members of the first class (clubs)

Add the members of the second class (jacks)

Then subtract (once) for anything that occurs in both

because those were counted twice.

If, instead, the problem were "black card" or "jack"

it would be

26 black cards

4 jacks

but Jack of Clubs and Jack of Spaces are in both

26 + 4 - 2.

If it were "face card" or "club":

13 clubs

4 x 3 face cards = 12

But 3 face cards are also clubs

13 + 12 - 3 = 22.