course Mth 151 ¥ãª™¬Ð¬N•Ï¦‰ÞÄ͟溱ñál´ô߀õ¿¬assignment #001
......!!!!!!!!...................................
12:13:37 `q001. Note that there are 4 questions in this assignment. `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? What numbers do B and A' have in common?
......!!!!!!!!...................................
RESPONSE --> B and A have the numbers 8,4, 2 in common B and A ' have the numbers 3, 5, 9, 1, 7 in common confidence assessment: 2
.................................................
......!!!!!!!!...................................
12:44:30 `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?
......!!!!!!!!...................................
RESPONSE --> I put down just the one number, not the full number for question one. I had the right idea but did not carry it out enough. q002: No confidence assessment: 1
.................................................
......!!!!!!!!...................................
12:45:18 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.
......!!!!!!!!...................................
RESPONSE --> I wasn't sure that there wasn't a way around it but I didn't think there was. self critique assessment: 3
.................................................
......!!!!!!!!...................................
12:46:03 `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?
......!!!!!!!!...................................
RESPONSE --> Some people with dark hair have blue eyes. confidence assessment: 3
.................................................
......!!!!!!!!...................................
12:46:17 The 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.
......!!!!!!!!...................................
RESPONSE --> self critique assessment: 3
.................................................
......!!!!!!!!...................................
12:46:59 `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?
......!!!!!!!!...................................
RESPONSE --> 10 confidence assessment: 3
.................................................
......!!!!!!!!...................................
12:47:05 Of the 30 red blocks 20 are cubical, so the rest must be cylindrical. This leaves 10 red cylindrical blocks.
......!!!!!!!!...................................
RESPONSE --> self critique assessment: 3
.................................................