Question

in the braces below, list all subsets of the set {6, 7}. 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 subset definition

A subset of a set \( S \) is a set whose elements are all in \( S \). The empty set \( \varnothing \) is a subset of every set. For a set with \( n \) elements, there are \( 2^n \) subsets. The set \( \{6, 7\} \) has \( n = 2 \) elements, so \( 2^2=4 \) subsets.

Step2: List subsets

• Empty set: \( \varnothing \)
• Subset with only 6: \( \{6\} \)
• Subset with only 7: \( \{7\} \)
• Subset with both 6 and 7: \( \{6, 7\} \)

Answer:

\(\varnothing, \{6\}, \{7\}, \{6, 7\}\)