Question

in the braces below, list all subsets of the set {3, 4, 5}. write each subset in your list in roster form. if there is more than one subset in your list, separate them with commas. if you need the empty set in your list, use the symbol ∅.

Explanation:

Step1: Recall the definition of a subset

A subset of a set \( S \) is a set that contains only elements from \( S \), including the empty set \( \varnothing \) and the set \( S \) itself. For a set with \( n \) elements, the number of subsets is \( 2^n \). Here, the set \( \{3, 4, 5\} \) has \( 3 \) elements, so the number of subsets is \( 2^3=8 \).

Step2: List the subsets

• Empty set: \( \varnothing \)
• Single - element subsets: \( \{3\} \), \( \{4\} \), \( \{5\} \)
• Two - element subsets: \( \{3, 4\} \), \( \{3, 5\} \), \( \{4, 5\} \)
• Three - element subset: \( \{3, 4, 5\} \)

Answer:

\( \varnothing, \{3\}, \{4\}, \{5\}, \{3, 4\}, \{3, 5\}, \{4, 5\}, \{3, 4, 5\} \)