1.2 Subsets

Set $L$ is a set of reading materials available in a shop at the airport, $L = \left\{\text{newspaper},\text{ magazine},\text{ book}\right\}$. List all the subsets of set $L$.

Consider the set of common political parties in the United States, $P = \left\{Democratic, Green, Libertarian, Republican\right\}$. Determine if the following sets are proper subsets of $P$.

1. $M = \left\{Democratic, Republican\right\}$
2. $G = \left\{Green\right\}$
3. $V = \left\{Republican, Libertarian, Green, Democratic\right\}$

Consider the subsets of a standard deck of cards: $S = \left\{spades, hearts, diamonds, clubs\right\}$; $R = \left\{hearts, diamonds\right\}$; $B = \left\{spades, clubs\right\}$; and $C = \left\{clubs\right\}$.

Express the relationship between the following sets symbolically.

1. Set $S$ and set $B$.
2. Set $C$ and set $B$.
3. Set $R$ and $R$.

Find the number of subsets of each of the following sets.

1. The set of top five scorers of all time in the NBA: $S = \left\{LeBron James, Kareem Abdul-Jabbar, Karl Malone, Kobe Bryant, Michael Jordan\right\} .$
2. The set of the top four bestselling albums of all time: $A = \left\{Thriller, Hotel California, The Beatles White Album, Led Zepplin IV\right\}$.
3. $R = \left\{Snap, Crackle, Pop\right\}$.

Using natural numbers, multiples of 3 are given by the sequence ${3, 6, 9, …}$. Write this set using set builder notation by expressing each multiple of 3 using a formula in terms of a natural number, $n$.

A fast-food restaurant offers a deal where you can select two options from the following set of four menu items for $6: a chicken sandwich, a fish sandwich, a cheeseburger, or 10 chicken nuggets. Javier and his friend Michael are each purchasing lunch using this deal. Create two equivalent, but not equal, subsets that Javier and Michael could choose to have for lunch.

A high school volleyball team at a small school consists of the following players: {Angie, Brenda, Colleen, Estella, Maya, Maria, Penny, Shantelle}. Create two possible equivalent starting line-ups of six players that the coach could select for the next game.