course Mth 151
6/6 7
Open QA3:*********************************************
Question: `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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Your solution:
A=20 B=12 n(A^B)= 8 and AUB= 27
3
Explain the circles from the previous question
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Question: `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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Your solution:
There are 7 people plus the 8 in the middle section that overlap so there are 15 people not in collection A so we call them A’ and there are 12 not in collection B plus the 8 that overlap so there are a total of 20 not in section B so we call them B’. A’ lacks dark hair because A is the ones with dark hair. B’ stands for those who lack bright eyes because B stands for those who have bright eyes.
2
Ok
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Question: `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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Your solution:
(A U B)’ are the people who lack either trait since A U B were the people who have at least one trait. There are 8 people in this category because you have a total of 35 in the room but there are only 27 that have one of the other of the traits. (A^B)’ are the people who have do not have both the characteristic but still have one so that means there are 27 people in this category because there are 27 in all the regions.
2
Ok
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Question: `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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Your solution:
There would be 27 people in A’ U B’ because there are 7 in A’ because those are the ones without dark hair and then there are 8+12 in A UB’ because those are the people left. A’^B’ would be 35 because it includes everyone because what is not in A and not in B is everyone.
1
Explain a little better because the way its worded is confusing
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Question: `q005. Succinctly describe the relationships between ( A U B ) ', A ' U B ', (A ^ B) ' and A ' ^ B '.
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Your solution:
(AUB)’ is the same as saying A’^B’ and (A^B)’ is the same as A’ U B’
1
Understand union and intersection a little better
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Due to a carelessly typed password, a block of files failed to post correctly on 6/7/10. This file was among them, and is being posted on 6/8/10, a day late.