#$&* course mth 151 9:30 pm ; 1/15/12 001. Sets
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Given Solution: Of the numbers in B, 8, 89, 104, 4321 each have at least one even digit and so are common to both sets. Of the numbers in B, 3 is odd, both of the digits in the number 35 are odd, as are all three digits in the number 357. All three of these numbers are therefore in A ' . STUDENT QUESTION In the second part of the question you said BOTH of these numbers are therefore in A’, so does that mean that 3 is not and if so then why not? Also what does the ‘ (is it an apostrophe?) in A’ stand for or is in just a means of separation? INSTRUCTOR RESPONSE Of the numbers in B, the number 3 is in A ', the number 35 is in A ' and the number 357 is in A ' . The apostrophe (you identified it correctly) indicates that you are looking for elements that are NOT in the set. This is in relation to the statement in the problem: Let A ' stand for the collection of all whole numbers which are not in the collection A. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ?????????????? In this question I was not sure if I am suppose to look at each number individually or look at them all as the numbers put together????? ------------------------------------------------ Self-critique Rating: 2
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 8 people have dark hair, 2 have red, and 9 have light brown, or blonde. 8+2+9= 19 people in the room. No there are 19 people in the room, not 17. Because they each have a different color hair. It said nobody has more than one hair color. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aIf we assume that dark brown, light brown or blonde, and bright red hair are mutually exclusive (i.e., someone can't be both one category and another, much less all three), then we have at least 8 + 2 + 9 = 19 people in the room, and it is not possible that we have exactly 17. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: ok ********************************************* Question: `q003. I have in a room 6 people with dark hair and 10 people with blue eyes. There are only 14 people in the room. But 10 + 6 = 16, which is more than 14. How can this be?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 6 people with dark hair in the room, 10 people with blue eyes. There are only 14 people in the room. The people with blue eyes don’t have to have dark hair. There is more categories. They must have been counted twice. So just subtract 2 people from the 16 total and get 14. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aThe key here is that there is nothing mutully exclusive about these categories-a person can have blue eyes as well as dark hair. So if there are 2 people in the room who have dark hair and blue eyes, which is certainly possible, then when we add 10 + 6 = 16 those two people would be counted twice, once among the 6 blue-eyed people and once among the 10 dark-haired people. So the 16 we get would be 2 too high. To get the correct number we would have to subtract the 2 people who were counted twice to get 16 - 2 = 14 people. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: ok ********************************************* Question: `q004. In a set of 100 child's blocks 60 blocks are cubical and 40 blocks are cylindrical. 30 of the blocks are red and 20 of the red blocks are cubical. How many of the cylindrical blocks are red?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: There are 100 blocks. 60 are cubical and 40 are Cylindrical. 30 are red and 20 of those are cubical. To find out the Cylindrical 100-60, which are cubical. = 40 cubical. 30 blocks are red and 20 of them are cubical. So 30-20= 10. 10 of the cylindrical blocks are red. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aOf the 30 red blocks 20 are cubical, so the rest must be cylindrical. This leaves 10 red cylindrical blocks. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: ok " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!