course Mth 151 ???{T???????G?w?assignment #003003. Intersection, Union, Complement, de Morgans Laws Liberal Arts Mathematics I 09-15-2007
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16:15:55 `q001. Note that there are 5 questions in this assignment. Again we have a total of 35 people in a room. Of these, 20 have dark hair and 15 have bright eyes. There are 8 people with dark hair and bright eyes. Let A stand for the collection of people who have dark hair and B for the collection who have bright eyes. The Intersection of these two collections is denoted A ^ B, and stands for the collection of all people who have both dark hair and bright eyes. The Union of these two collections is denoted A U B, and stands for the collection of all people who have at least one of these characteristics. In terms of the diagram you made for the preceding problem, describe the collection A ^ B and the collection A U B. Give the number of people in each of these collections (these numbers are designated by the notation n ( A ^ B) and n(A U B) ). Refer to the diagrams you have made.
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RESPONSE --> A - dark hair - 20 people B - bright eyes - 15 A ^ B - both - 8 A U B - with at least on characterist Collection A ^ B has the number with both characteristics so it would contain 8 people. Collection A U B would has would contain 27 because there are 35 people and 8 who have both so 35 - 8 = 27. confidence assessment: 2
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16:22:34 `q002. Continuing the preceding example, we let A' stand for the people who are not in the collection A, and we let B' stand for the people who are not in the collection B. What are the characteristics of the people in A', and what characterizes people in B' ? What are n(A ') and n(B '), the numbers of people in A' and B' ?
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RESPONSE --> Since A' are not people who are in collection A n(A') would be the people who are in B - 7 people and B' does not include the people in B so n(B') would be the people in A - 12 people. confidence assessment: 2
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16:34:23 `q003. ( A U B ) ' stands for the everyone outside A U B, and ( A ^ B ) ' stands for everyone outside A ^ B. What characterizes the people in each of these collections, and how many people are there in each?
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RESPONSE --> The characterists of the collection ( A U B) is everyone outside of A U B, (A U B) would contain the people who have both dark hair and bright eyes consisting of 8 people and the people in (A ^ B) are outside of A ^ B would contain the people who does not have both dark hair and bright eyes consisting of 27 people confidence assessment: 2
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" 10:10:26 `q004. How many people are in A ' U B ', and how could those people be characterized? Answer the same for A ' ^ B '.
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RESPONSE --> The people who would be in collection A' U B' would be all of the people who have either dark hair or bright eyes, A' U B' would be 27 people. The people who would be in collection A' ^ B' would include the people who have both dark hard and bright eyes, A' ^ B' would be 8 people. confidence assessment: 2
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10:35:38 `q005. Succinctly describe the relationships between ( A U B ) ', A ' U B ', (A ^ B) ' and A ' ^ B '.
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RESPONSE --> The relationship between (A U B)', A' U B', (A ^ B)' and A ' ^ B ' is the the order in which you perform the operation. The ( ) is done first in both operations. confidence assessment: 2
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