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 that contain the element .
Step-by-Step Solution:
The original set is , and we are required to find the subsets that contain . The remaining elements are , , and . We can choose any combination of these remaining elements to form subsets.
The possible combinations are:
- No elements from (just ).
- One element from .
- Two elements from .
- All three elements from .
So the subsets containing are:
List of all subsets containing :
Would you like any further details or clarifications?
Here are 5 related questions:
- How many subsets does a set of elements have?
- What are the subsets of a set that does not contain a specific element?
- How can we calculate the power set of a given set?
- What is the difference between a proper subset and an improper subset?
- Can we generalize this process for any given set and any specific element?
Tip: The total number of subsets of a set with elements is , 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