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# Sets & Counting: Exercises on Sets (Math Problem Sample)

Instructions:

Sets & Counting
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.
Assignment Expectations:
Clearly define sets and set operations.
Select appropriate set elements and distinquish between sets, subsets, and proper subsets.
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Content:

1. Definitions

Set

A well defined collection of (distinct) objects is called a set

Subset

If A & B are two sets, A is called a subset of B, written A ( B, if, and only if, any element of A is also an element of B

Proper Subset

Let A and B be sets. A is a proper subset of B, if, and only if, every element of A is in B but there is at least one element of B that is not in A, and is denoted as A ( B

Complement of a Set

Let A be a subset of universal set U. The complement of A is the set of all elements in U that do not belong to A, and is denoted Ac

Union of a Set

Let A and B be subsets of a universal set U. The union of sets A and B is the set of all elements in U that belong to A or to B or to both, and is denoted A ( B

Intersection of a Set

Let A and B subsets of a universal set U. The intersection of sets A and B is the set of all elements in U that belong to both A and B and is denoted A ( B

2. Problems

X = {3, 7,...

Set

A well defined collection of (distinct) objects is called a set

Subset

If A & B are two sets, A is called a subset of B, written A ( B, if, and only if, any element of A is also an element of B

Proper Subset

Let A and B be sets. A is a proper subset of B, if, and only if, every element of A is in B but there is at least one element of B that is not in A, and is denoted as A ( B

Complement of a Set

Let A be a subset of universal set U. The complement of A is the set of all elements in U that do not belong to A, and is denoted Ac

Union of a Set

Let A and B be subsets of a universal set U. The union of sets A and B is the set of all elements in U that belong to A or to B or to both, and is denoted A ( B

Intersection of a Set

Let A and B subsets of a universal set U. The intersection of sets A and B is the set of all elements in U that belong to both A and B and is denoted A ( B

2. Problems

X = {3, 7,...

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