Questions: In the braces below, list all subsets of the set 6,5,4. 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 ∅.

In the braces below, list all subsets of the set 6,5,4. 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 ∅.

Transcript text: In the braces below, list all subsets of the set $\{6,5,4\}$. 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 $\varnothing$.

Solution

Solution Steps

To list all subsets of a given set, we need to consider all possible combinations of its elements, including the empty set and the set itself. For a set with $ n $ elements, there are $ 2^n $ subsets.

Step 1: Identify the Set

The given set is $ S = \{6, 5, 4\} $.

Step 2: Calculate the Number of Subsets

The number of subsets of a set with $ n $ elements is given by $ 2^n $. Here, $ n = 3 $, so the number of subsets is: \[ 2^3 = 8 \]

Step 3: List All Subsets

The subsets of the set $ S $ are as follows: