Question

list all the subsets of the given set. {f, p, w} choose the answer that lists all of the subsets of {f, p, w}. a. {f}, {p}, {w}, {f, p}, {f, w}, {p, w} b. {}, {f}, {p}, {w}, {f, p}, {f, w}, {p, w}, {f, p, w} c. {f}, {p}, {w}, {f, p}, {f, w}, {p, w}, {f, p, w} d. {}, {f}, {p}, {w}, {f, p}, {f, w}, {p, w}

Explanation:

Step1: Recall subset definition

A subset includes the empty set $\{\}$ and all combinations of the set's elements, including the set itself.

Step2: List all subsets of $\{f,p,w\}$

• Empty set: $\{\}$
• Single-element subsets: $\{f\}, \{p\}, \{w\}$
• Two-element subsets: $\{f,p\}, \{f,w\}, \{p,w\}$
• Full set: $\{f,p,w\}$

Step3: Match to options

Compare the complete list to the given choices.

Answer:

B. $\{\}$, $\{f\}$, $\{p\}$, $\{w\}$, $\{f, p\}$, $\{f, w\}$, $\{p, w\}$, $\{f, p, w\}$