# Exercises on Sets

Exercises on Sets

1. Please provide a short definition of the following:

a. Set

b. Subset

c. Proper Subset

d. Compliment 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 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.

Assignment Expectations:

Clearly define sets and set operations.

Select appropriate set elements and distinquish between sets, subsets, and proper subsets.

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#### Solution Preview

Hi,

1.

a. A set is a finite or infinite collection of related elements or objects regardless of the order. Examples of sets are collection of numbers, collection of alphabets, collection of toys, collection of country names, and collection of colors.

b. A subset is a set in which all of its elements are also contained in a general set. For example Set A contains {1, 3, 5, 7}. Set B contains {1, 5}. Set B is a subset of the general set A.

c. A proper subset is a type of subset in which all of its elements are contained in the general set, but not ...

#### Solution Summary

This posting contains the solution to the given problems.