Algebra Know-It-ALL

Here, the intersection set has four elements:

W 3 −∩W0+= {0, 1, 2, 3}

Figure 2-4 is a Venn diagram that shows two overlapping sets. Think of V as the rectangle
and everything inside it. Imagine W as the oval and everything inside it. The two regions
are hatched diagonally, but in different directions. The intersection V∩W shows up as a
double-hatched region.

Are you confused?

Go back and look again at Fig. 2-1. You can see that the set of all women in Chicago (call it Cw) is a proper
subset of the set of all people in the state of Illinois (call it Ip). You would write down this fact as follows:

Cw⊂Ip

The diagram also makes it clear that the intersection of set Cw with set Ip is just the set Cw. In order to be
in both sets, a person must be a woman in Chicago, that is, an element of Cw. Here’s how you would write
that

Cw∩Ip=Cw

You can always draw a Venn diagram if it will help you understand how sets are related.

Here’s a challenge!

Find two sets of whole numbers that overlap, with neither set being a subset of the other, and whose inter-
section set contains infinitely many elements.

Set Intersection 29

Universe

V

W

V

U

W

Figure 2-4 Two overlapping sets, V and W. Their

intersection is shown by the double-hatched

region.