#$&* course Mth 151 Question: `q001. Let A stand for the collection of all whole numbers which have at least one even digit (e.g., 237, 864, 6, 3972 are in the collection, while 397, 135, 1, 9937 are not). Let A ' stand for the collection of all whole numbers which are not in the collection A. Let B stand for the collection { 3, 8, 35, 89, 104, 357, 4321 }. •What numbers do B and A have in common?
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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): I was breaking down all of the numbers. I was not really sure what was being asked. ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q002. I have in a room 8 people with dark hair brown, 2 people with bright red hair, and 9 people with light brown or blonde hair. Nobody has more than one hair color. Is it possible that there are exactly 17 people in the room?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: No it is not, simple because no one has more than one color hair. All together that is 19 people. So I do not believe that at any point there could be 17 people in the room. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `If 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): ------------------------------------------------ Self-critique Rating: ********************************************* 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: I did 16 - 2 and got 14. So that means that 2 of the 6 with dark hair must also have blue eyes. That leaves 8 with just blue eyes and 4 with just dark hair. 2 + 4 + 8 = 14. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `aThe key here is that there is nothing mutully exclusive about these categories-a person can have blue eyes as well as dark hair. So if there are 2 people in the room who have dark hair and blue eyes, which is certainly possible, then when we add 10 + 6 = 16 those two people would be counted twice, once among the 6 blue-eyed people and once among the 10 dark-haired people. So the 16 we get would be 2 too high. To get the correct number we would have to subtract the 2 people who were counted twice to get 16 - 2 = 14 people. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Self-critique Rating: ********************************************* Question: `q004. In a set of 100 child's blocks 60 blocks are cubical and 40 blocks are cylindrical. 30 of the blocks are red and 20 of the red blocks are cubical. How many of the cylindrical blocks are red?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Only 10 of the cylindrical blocks are red. This only possible because 30 all together are red and 20 of them are cubical. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): ------------------------------------------------ Self-critique Rating: " end document Self-critique (if necessary): ------------------------------------------------ Self-critique rating: