Algebra Know-It-ALL

146 Review Questions and Answers

Question 2-5

What does the hatched region in Fig. 10-1 represent?

Answer 2-5

It portrays the set of elements belonging to both P and Q. That’s the intersection of the two

sets, written P∩Q.

Question 2-6

What’s the union of two disjoint sets X and Y? What’s the intersection of two disjoint setsX

andY?

Answer 2-6

The union of two sets X and Y is the set of all elements in either X or Y. Their intersection is

the set of elements in both X and Y. If X and Y are disjoint, then there are no elements belong-

ing to them both, so the intersection is the null set.

Question 2-7

What’s the union of two congruent sets? The intersection of two congruent sets?

Answer 2-7

By definition, if two sets X and Y are congruent, then they have exactly the same elements.

Every element in X is also in Y, and every element in Y is also in X. The two sets overlap

totally. Their union is the set of all elements in either X or Y. That’s the same as either X or Y

by itself. Their intersection is the set of elements in both X and Y. That’s also the same as either

X or Y by itself. In this case, all the following sets are identical:

X

Y

X∪Y

X∩Y

Question 2-8

Can a set be a subset of itself? A proper subset of itself?

Answer 2-8

Any set is a subset of itself. But no set is a proper subset of itself. By definition, a proper subset

of any set S can’t contain all of the elements in S.

Question 2-9

Is there any set that is a subset of every possible set?

Answer 2-9

Yes. The null set is a subset of any set we can imagine, even itself.