Math Problem Statement

List all the subsets of {a, b, c, d} containing a.

Solution

The problem asks to list all the subsets of the set {a,b,c,d}\{a, b, c, d\} that contain the element aa.

Step-by-Step Solution:

The original set is {a,b,c,d}\{a, b, c, d\}, and we are required to find the subsets that contain aa. The remaining elements are bb, cc, and dd. We can choose any combination of these remaining elements to form subsets.

The possible combinations are:

  • No elements from {b,c,d}\{b, c, d\} (just aa).
  • One element from {b,c,d}\{b, c, d\}.
  • Two elements from {b,c,d}\{b, c, d\}.
  • All three elements from {b,c,d}\{b, c, d\}.

So the subsets containing aa are:

  1. {a}\{a\}
  2. {a,b}\{a, b\}
  3. {a,c}\{a, c\}
  4. {a,d}\{a, d\}
  5. {a,b,c}\{a, b, c\}
  6. {a,b,d}\{a, b, d\}
  7. {a,c,d}\{a, c, d\}
  8. {a,b,c,d}\{a, b, c, d\}

List of all subsets containing aa:

  • {a}\{a\}
  • {a,b}\{a, b\}
  • {a,c}\{a, c\}
  • {a,d}\{a, d\}
  • {a,b,c}\{a, b, c\}
  • {a,b,d}\{a, b, d\}
  • {a,c,d}\{a, c, d\}
  • {a,b,c,d}\{a, b, c, d\}

Would you like any further details or clarifications?

Here are 5 related questions:

  1. How many subsets does a set of nn elements have?
  2. What are the subsets of a set that does not contain a specific element?
  3. How can we calculate the power set of a given set?
  4. What is the difference between a proper subset and an improper subset?
  5. Can we generalize this process for any given set and any specific element?

Tip: The total number of subsets of a set with nn elements is 2n2^n, including the empty set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Subsets

Formulas

Subset formula: 2^n subsets for a set with n elements

Theorems

Power Set Theorem

Suitable Grade Level

Grades 6-8