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# Algebra 1 Item No 06

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Union and Intersection

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### Algebra 1 Item No 06

1. 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. 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. 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. 4. We can also write them in roster form like the ones we have in our question. www.upcatreview.com
5. 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. 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. 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. 8. In the question, we are asked to find (a ∪ b) ∩ c. www.upcatreview.com
9. 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. 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. 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. 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. 13. The answer is: D. none of these www.upcatreview.com