Another operation that can be defined on sets A and B is the difference of the sets, denoted by
A − B.
Here is the formal definition of the difference of sets A and B.
A − B = {x | x is in A  and  x not in B}
Thus
A − B
is the set of elements that belong to A but not to B. For instance, let
A = {1, 2, 3, 7, 8}
and
B = {2, 7, 11}.
Then
A − B = {1, 3, 8}.

Determine the difference, given that
U = {1, 2, 3, 4, 5, 6, 7, 8, 9},

A = {2, 4, 6, 8},
and
B = {1, 4, 8, 9}.
(Enter your answers as a comma-separated list.)
B − A

The difference \( B - A \) is the set of elements that are in \( B \) but not in \( A \).

We are given:

- \( A = \{2, 4, 6, 8\} \)
- \( B = \{1, 4, 8, 9\} \)

To find \( B - A \), we look for elements that are in \( B \) but **not** in \( A \).

Comparing the sets:
- The element 1 is in \( B \) and not in \( A \).
- The element 4 is in both \( B \) and \( A \) (so it’s excluded).
- The element 8 is in both \( B \) and \( A \) (so it’s excluded).
- The element 9 is in \( B \) and not in \( A \).

Therefore, \( B - A = \{1, 9\} \).

So, the difference \( B - A \) is:
\[
1, 9
\]

Would you like more details on this? Here are 5 related questions:

1. What is the difference \( A - B \) using the same sets?
2. How would the difference operation change if the sets were larger?
3. Can you find the symmetric difference of \( A \) and \( B \)?
4. What is the intersection of sets \( A \) and \( B \)?
5. How would you represent the union of \( A \) and \( B \)?

**Tip:** Set operations are fundamental in understanding relationships between different groups of elements in mathematics and computer science.

Determine the difference, given that U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}, and B = {1, 4, 8, 9}. (Enter your answers as a comma-separated list.) B − A

Explore how to find the difference of sets B - A using set theory. Learn the step-by-step method to determine which elements belong to set B but not to set A, with clear examples. This concept is ideal for students in Grades 6-8.

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