Math Problem Statement

Find the number of subsets of the given set. {2, 11, 6} subsets

Solution

To find the number of subsets of a given set, we use the formula:

Number of subsets=2n\text{Number of subsets} = 2^n

where nn is the number of elements in the set.

For the set {2,11,6}\{2, 11, 6\}, there are 3 elements. So, we have:

Number of subsets=23=8\text{Number of subsets} = 2^3 = 8

Therefore, the set {2,11,6}\{2, 11, 6\} has 8 subsets.

List of all subsets:

  1. {}\{\} (the empty set)
  2. {2}\{2\}
  3. {11}\{11\}
  4. {6}\{6\}
  5. {2,11}\{2, 11\}
  6. {2,6}\{2, 6\}
  7. {11,6}\{11, 6\}
  8. {2,11,6}\{2, 11, 6\}

Would you like more details or have any questions?

Here are some related questions:

  1. What is the formula to find the number of subsets of a set with nn elements?
  2. How many subsets does a set with 4 elements have?
  3. What is the difference between a proper subset and an improper subset?
  4. How do we find the number of proper subsets of a set?
  5. What is the power set of a given set?

Tip: Remember, the empty set is always a subset of any set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Subsets
Combinatorics

Formulas

Number of subsets = 2^n

Theorems

Power Set Theorem

Suitable Grade Level

Grades 6-8