Questions: List all the subsets of the given set. 0 The subsets are (Use a comma to separate answers as needed.)

List all the subsets of the given set. 0

The subsets are 
(Use a comma to separate answers as needed.)
Transcript text: List all the subsets of the given set. \{0\} The subsets are $\square$ (Use a comma to separate answers as needed.)
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Solution

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Solution Steps

To list all the 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 Given Set

The given set is \( \{0\} \).

Step 2: Determine the Number of Subsets

For a set with \( n \) elements, the number of subsets is \( 2^n \). Here, \( n = 1 \), so the number of subsets is \( 2^1 = 2 \).

Step 3: List All Subsets

The subsets of the set \( \{0\} \) are:

  1. The empty set: \( \emptyset \)
  2. The set itself: \( \{0\} \)

Final Answer

The subsets are \( \boxed{\emptyset, \{0\}} \).

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