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.