Math Problem Statement

List all the subsets of the given set: {b, o, s}

Solution

The question asks to list all the subsets of the set {b,o,s}\{b, o, s\}.

Given a set with nn elements, the number of subsets is 2n2^n. For the set {b,o,s}\{b, o, s\}, there are 3 elements, so the number of subsets is 23=82^3 = 8.

The subsets are as follows:

  1. {}\{\} (the empty set)
  2. {b}\{b\}
  3. {o}\{o\}
  4. {s}\{s\}
  5. {b,o}\{b, o\}
  6. {b,s}\{b, s\}
  7. {o,s}\{o, s\}
  8. {b,o,s}\{b, o, s\}

Let me know if you would like further details on this topic or explanations for any steps.

Here are 5 related questions to expand your understanding:

  1. How do you find the number of subsets for a set with nn elements?
  2. What is the difference between a proper subset and a subset?
  3. How would you list the subsets of a 4-element set?
  4. Can you explain the concept of a power set?
  5. What are the subsets of the set {1,2}\{1, 2\}?

Tip: The power set of any set includes all possible combinations of its elements, including the empty set and the set itself.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Subsets

Formulas

Number of subsets of a set: 2^n, where n is the number of elements in the set

Theorems

Power set theorem

Suitable Grade Level

Grades 7-8