# Set Definitions with Unions and Intersections

Exercises on Sets

1. Please provide a short definition of the following:

a. Set

b. Subset

c. Proper Subset

d. Complement of a set

e. Union of a set

f. Intersection of a set

Solve following problems showing your work:

2. Set X = {3, 7, 11, 21, 39, 43, 567}, Set Y = {1, 3, 6, 8, 11, 42, 567}

a. What is the union of Sets X and Y?

b. What is the intersection of Sets X and Y

c. Create your own set Z that is a proper subset of Set X.

3. Let Set 1 be the entire alphabet. Let Set 2 = {m, n, o, p, q, r}

a. What is the complement of Set 2 in Set 1?

b. Set 3 = {n, o, p, q}. Is Set 3 a proper subset of Set 2? Explain your reasoning.

4. Take out a coin for the following problems:

a. Suppose you are going to flip a coin once. What is the set of possible outcomes for this?

b. Suppose you are going to flip a coin twice. What is the set of possible outcomes for this?

c. If you flip a coin twice, what are the chances that you will get one head and one tail (i.e. one in three, one in four, etc.)? Use your answer to the question 3b to get your answer.

https://brainmass.com/math/combinatorics/set-definitions-unions-intersections-308775

#### Solution Preview

1. Short definitions

a. Set - A collection or group of objects. The elements or objects in a set are usually grouped in braces (i.e. {a,b,c}).

b. Subset - A set containing the original elements of the set or only part of the elements of the original set.

c. Proper Subset - A set containing original elements of a set, but this type of set does not contain all of the elements of a set. A subset can be an exact copy of the original set, containing all of the same elements. But a proper subset must contain fewer elements than the original set.

d. Compliment of a set - A set containing ...

#### Solution Summary

In this solution, brief definitions are given on the topics of sets, subsets, intersections, and the unions of sets. Furthermore, when given two sets, intersections and unions are found.

Mathematics: Union, Intersection, and Complements

1. Match the word and definition or symbol.

____ A. Union 1. {}

____ B. Intersection 2. A' U B'

____ C. Complement 3. '

____ D. Empty Set 4. A' ∩ B'

____ E. (A ∩ B)' 5. ∩

____ F. (A U B)' 6. U

2. Two sets are disjoint if their intersection is a null set.

If set A = {1,2,3,4,5,6}, set B = {2,3,4,5,8,9} and the Universal set = {1,2,3,4,5,6,7,8,9,10}, then answer the following:

3. A ∩ B = {2, 3, 4, 5}

4. A U B = {1, 2, 3, 4, 5, 6, 8, 9}

5. A' = {7, 8, 9, 10}

6. A' ∩ B' = {7, 10}

7. |A| = 6

8. What is the complement of the Universal Set = { } (Please see the attachment)

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