https://file.aiquickdraw.com/mathbot/file/1726402761102rnka38df.jpg

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

### Step-by-Step Solution:

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

The possible combinations are:
- No elements from \( \{b, c, d\} \) (just \( a \)).
- One element from \( \{b, c, d\} \).
- Two elements from \( \{b, c, d\} \).
- All three elements from \( \{b, c, d\} \).

So the subsets containing \( a \) are:
1. \( \{a\} \)
2. \( \{a, b\} \)
3. \( \{a, c\} \)
4. \( \{a, d\} \)
5. \( \{a, b, c\} \)
6. \( \{a, b, d\} \)
7. \( \{a, c, d\} \)
8. \( \{a, b, c, d\} \)

### List of all subsets containing \( a \):
- \( \{a\} \)
- \( \{a, b\} \)
- \( \{a, c\} \)
- \( \{a, d\} \)
- \( \{a, b, c\} \)
- \( \{a, b, d\} \)
- \( \{a, c, d\} \)
- \( \{a, b, c, d\} \)

Would you like any further details or clarifications?

Here are 5 related questions:
1. How many subsets does a set of \( n \) 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 \( n \) elements is \( 2^n \), including the empty set.

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

Learn how to list all the subsets of the set {a, b, c, d} that contain the element 'a'. This problem explores the basics of set theory, focusing on subsets and the power set. Ideal for middle school students studying set theory.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation