The document defines sets a, b, and c as collections of numbers. It finds the union of sets a and b, which is the combination of all numbers in both sets. It then finds the intersection of the union of a and b with set c. The intersection contains elements that are common to both sets. However, there are no common elements between the union of a and b ({1, 3, 5, 7, 9, 11}) and c ({2, 4, 6, 8}). Therefore, the result is an empty set, which is not one of the answer choices given. The answer is D. none of these.

1. Algebra 1 Item No. 6Algebra 1 Item No. 6
If a = {1, 3, 5, 7}, b = {5, 7, 9, 11}, c = {2, 4,
6, 8}. Find (a ∪ b) ∩ c.
A. {5, 7}
B. {1, 2, 3, 4}
C. {5, 6, 7, 8}
D. none of these
www.upcatreview.com

2. First, let define some terms:
A set is a collection of objects. For our case, we’ll
have numbers as our objects.
www.upcatreview.com

3. First, let define some terms:
A set is a collection of objects. For our case, we’ll
have numbers as our objects.
Sets can be written in descriptive form.
For example, Set N is the set of all counting numbers.
www.upcatreview.com

4. We can also write them in roster form like the
ones we have in our question.
www.upcatreview.com

5. We can also write them in roster form like the
ones we have in our question.
When writing in roster form, we use braces, { },
to enclose the collection.
For example, {3, 6, 9, 12}
www.upcatreview.com

6. The union of two sets A and B, denoted by A ∪
B, is the set of all elements that are contained
in sets A, B or both.
www.upcatreview.com

7. The union of two sets A and B, denoted by A ∪
B, is the set of all elements that are contained
in sets A, B or both.
The intersection of two sets A and B, denoted as
A ∩ B, is the set of all elements that belong to
both sets A and B.
www.upcatreview.com

8. In the question, we are asked to find
(a ∪ b) ∩ c.
www.upcatreview.com

9. In the question, we are asked to find
(a ∪ b) ∩ c.
Let us find (a ∪ b) first:
a = {1, 3, 5, 7} b = {5, 7, 9, 11}
Combining these two sets, we get:
(a ∪ b) = {1, 3, 5, 7, 9, 11}Note that we only have
to write 5 and 7 once.
www.upcatreview.com

10. Now let’s find the whole thing, (a ∪ b) ∩ c:
(a ∪ b) = {1, 3, 5, 7, 9, 11}
c = {2, 4, 6, 8}
www.upcatreview.com

11. Now let’s find the whole thing, (a ∪ b) ∩ c:
(a ∪ b) = {1, 3, 5, 7, 9, 11}
c = {2, 4, 6, 8}
You would notice that there are no
elements common to both (a ∪ b) and c.
So the result is an empty set. The answer
cannot be found in the choices.An empty set is a set that has
no elements. It can be denoted
by { } or Ø
www.upcatreview.com

12. Algebra 1 Item No. 6Algebra 1 Item No. 6
If a = {1, 3, 5, 7}, b = {5, 7, 9, 11}, c = {2, 4,
6, 8}. Find (a ∪ b) ∩ c.
A. {5, 7}
B. {1, 2, 3, 4}
C. {5, 6, 7, 8}
D. none of these
www.upcatreview.com

13. The answer is:
D. none of these
www.upcatreview.com