List all the subsets of the given set. {g, k, v} Choose the answer that lists all of the subsets of {g, k, v}. O A. {g}, {k}, {v}, {g, k}, {g, v}, {k, v} B. {g), {k}, {v}, {g, k}, {g, v}, {k, v}, {g, k, v} OC. {}, {g}, {k}, {v}, {g, k}, {g, v}, {k, v} O D. {), {g}, {k}, {V}, {g, k}, {g, v}, {k, v}, {g, k, v}

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
Section: Chapter Questions
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**List all the subsets of the given set.**

Given Set: \(\{g, k, v\}\)

**Choose the answer that lists all of the subsets of \(\{g, k, v\}\).**

- **A.** \(\{\}, \{k\}, \{v\}, \{g, k\}, \{g, v\}, \{k, v\}\)
- **B.** \(\{g\}, \{k\}, \{v\}, \{g, k\}, \{g, v\}, \{k, v\}, \{g, k, v\}\)
- **C.** \(\{\}, \{g\}, \{k\}, \{v\}, \{g, k\}, \{g, v\}, \{k, v\}\)
- **D.** \(\{\}, \{g\}, \{k\}, \{v\}, \{g, k\}, \{g, v\}, \{k, v\}, \{g, k, v\}\)

**Explanation:**

Each subset of a set is formed by including or excluding each element. For the set \(\{g, k, v\}\), the total number of subsets is \(2^3 = 8\), including:

1. The empty set: \(\{\}\)
2. Single-element subsets: \(\{g\}, \{k\}, \{v\}\)
3. Two-element subsets: \(\{g, k\}, \{g, v\}, \{k, v\}\)
4. The full set itself: \(\{g, k, v\}\)

**Correct Answer: D**
Transcribed Image Text:**List all the subsets of the given set.** Given Set: \(\{g, k, v\}\) **Choose the answer that lists all of the subsets of \(\{g, k, v\}\).** - **A.** \(\{\}, \{k\}, \{v\}, \{g, k\}, \{g, v\}, \{k, v\}\) - **B.** \(\{g\}, \{k\}, \{v\}, \{g, k\}, \{g, v\}, \{k, v\}, \{g, k, v\}\) - **C.** \(\{\}, \{g\}, \{k\}, \{v\}, \{g, k\}, \{g, v\}, \{k, v\}\) - **D.** \(\{\}, \{g\}, \{k\}, \{v\}, \{g, k\}, \{g, v\}, \{k, v\}, \{g, k, v\}\) **Explanation:** Each subset of a set is formed by including or excluding each element. For the set \(\{g, k, v\}\), the total number of subsets is \(2^3 = 8\), including: 1. The empty set: \(\{\}\) 2. Single-element subsets: \(\{g\}, \{k\}, \{v\}\) 3. Two-element subsets: \(\{g, k\}, \{g, v\}, \{k, v\}\) 4. The full set itself: \(\{g, k, v\}\) **Correct Answer: D**
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