The expression \( \{ a + b \ | \ a \in B, \ b \in \{1, 3\} \} \) represents a set where every element is the sum of some \( a \in B \) and some \( b \in \{1, 3\} \).

To break it down:

- \( a \in B \): The element \( a \) comes from the set \( B \) (which hasn't been defined yet in this problem).
- \( b \in \{1, 3\} \): The element \( b \) is taken from the set \( \{1, 3\} \), which consists of the numbers 1 and 3.
- The expression \( a + b \) forms a new set by adding \( a \) from set \( B \) to each \( b \in \{1, 3\} \).

This construction generates a new set where each element is of the form \( a + 1 \) or \( a + 3 \), for each \( a \in B \).

If you provide a definition for \( B \), I can help you compute the resulting set.

Do you want details or have any questions?

Here are 5 related questions:
1. How does the definition of set \( B \) affect the resulting set \( \{a + b | a \in B, b \in \{1, 3\} \} \)?
2. What would be the resulting set if \( B \) were, for example, \( B = \{0, 2, 4\} \)?
3. How does set-builder notation work for more complex expressions involving more variables?
4. Can you define a set where the operation inside the set-builder notation is multiplication instead of addition?
5. What is the relationship between this operation and Cartesian products of sets?

**Tip**: Set-builder notation is a powerful way to describe sets, especially when dealing with infinite sets or more complex operations on elements.

Explore the concept of set-builder notation with the example {a + b | a ∈ B, b ∈ {1, 3}}. Learn how to form new sets by adding elements from one set to fixed elements from another set. This explanation is suitable for high school students and involves core set theory concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation