# Sets and Probability

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 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.

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#### Solution Preview

1. a). A set is a collection of different objects which are usually called elements of the set.

b). A subset of another set is a set whose elements are also elements of the other set.

c). A proper subset of another set is a subset of the other set, AND for which the other set has more elements than this subset does.

d). The complement of a set in another set is a set of elements that are not contained in this set but that are contained in the other set.

e). The union of two sets is a set that contains elements of these two sets put together, but ...

#### Solution Summary

This solution clearly addresses 4 problems on sets; the first 3 are purely on the topic of sets (including problems on subsets, proper subsets, intersections and unions of two sets, complements of sets, etc) while the 4th problem involves the topic of probability (looking for the set of possible outcomes when a coin is flipped once and/or twice).