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
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2. First, let define some terms:
A set is a collection of objects. For our case, we’ll
have numbers as our objects.
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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.
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4. We can also write them in roster form like the
ones we have in our question.
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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}
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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.
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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.
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8. In the question, we are asked to find
(a ∪ b) ∩ c.
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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.
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10. Now let’s find the whole thing, (a ∪ b) ∩ c:
(a ∪ b) = {1, 3, 5, 7, 9, 11}
c = {2, 4, 6, 8}
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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
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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
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