1.1 Basic Set Concepts

Write a set consisting of your three favorite sports and label it with a capital $S$.

For each of the following collections, determine if it represents a well-defined set.

1. The group of all past vice presidents of the United States.
2. A group of old cats.

Represent each of the following sets symbolically.

1. The set of prime numbers less than 2.
2. The set of birds that are also mammals.

Write the set of even natural numbers including and between 2 and 100, and label it with a capital $E$. Include an ellipsis.

Write the set of integers using the roster method, and label it with a $\mathbb{Z}$.

Using set builder notation, write the set $B$ of all types of balls. Explain what the notation means.

Consider the set of letters in the word “happy.” Determine the best way to represent this set, and then write the set using either the roster method or set builder notation, whichever is more appropriate.

Write the cardinal value of each of the following sets in symbolic form.

1. $F = \left\{\text{fork},\text{ spoon},\text{ knife},\text{ meat thermometer},\text{ can opener}\right\}$
2. The empty set.

Classify each of the following sets as infinite or finite.

1. $E = \left\{2 , 4 , 6 , 8 , 10\right\}$
2. $A$ is the set of lowercase letters of the English Alphabet, $A = \left\{a , b , c , \ldots , z\right\}$.
3. $\mathbb{Q} = \left\{\frac{p}{q} \left|\right. p and q are integers and q \neq 0\right\}$

Determine if the following pairs of sets are equal, equivalent, or neither.

1. $E = \left\{2 , 4 , 6 , 8 , 10\right\}$ and $F = \left\{fork, spoon, knife, meat thermometer, can opener\right\}$
2. The empty set and the set of prime numbers less than 2.
3. The set of vowels in the word happiness and the set of consonants in the word happiness.