Algebra Know-It-ALL

Once in a while, you’ll see a three-barred equals sign to indicate that two sets are congruent.
In this case, we would write

E≡F

Disjoint sets

When two sets are completely different, having no elements in common whatsoever, then
they are called disjoint sets. Here is an example of two disjoint sets of numbers:

G= {1, 2, 3, 4}

H= {5, 6, 7, 8}

Both of these sets are finite. But infinite sets can also be disjoint. Take the set of all the even
whole numbers and all the odd whole numbers:

Weven = {0, 2, 4, 6, 8, ...}

Wodd = {1, 3, 5, 7, 9, ...}

No matter how far out along the list for Weven you go, you’ll never find any element that is also
inWodd. No matter how far out along the list for Wodd you go, you’ll never find any element
that is also in Weven. We won’t try to prove this right now, but you should not have any trouble
sensing that it’s a fact. Sometimes the mind’s eye can see forever!
Figure 2-2 is a Venn diagram showing two sets, J and K, with no elements in common.
You can imagine J as the set of all the points on or inside the circle and K as the set of all the
points on or inside the oval. Sets J and K are disjoint. When you have two disjoint sets, neither
of them is a subset of the other.

How Sets Relate 25

Universe

J

K

Figure 2-2 Two disjoint sets, J and K. They have no

elements in common.