Algebra Know-It-ALL

Question 2-2

What’s the difference, if any, between the following sets?

A= {x,y,z}

B= {z,y,x}

C= {y,z,x}

D= {x,y,z,y,x}

E= {y,x,z,z,z,z,z, ...}

Answer 2-2

These sets are all the same. When the elements of a set are listed, the order of the list isn’t
important. Once we’ve listed something as an element of a set, we can list it again, or 10 times
more, or even infinitely many times, and it doesn’t matter.

Question 2-3

Imagine two sets, one called R and the other called S. They share three elements, called x, y,
andz. However, they both contain elements other than x, y, or z. What name can we give to
the set {x, y, z}?

Answer 2-3

The set {x, y, z} contains all the elements that belong to both R and S. By definition, the set
{x, y, z} is the intersection of R and S, written R∩S.

Question 2-4

What does the entire gray shaded region in Fig. 10-1 represent?

Answer 2-4

This region represents the set of all elements in set P, set Q, or both. That’s the union of sets
P and Q, written P∪Q.

P

Q

Figure 10-1 Illustration for

Questions and

Answers 2-4 and 2-5.

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