# hmk2 - COT 3100 Section 2 Homework#2 Fall 2000 Lecturer...

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COT 3100 Section 2 Homework #2 Fall 2000 Lecturer: Arup Guha Assigned: 9/12/00 Due: 9/21/00 in lecture 1) Determine all of the elements in the following sets: a) {((-2) n + 2 n )/2 | n {0, 1, 2, 3, 4}} b) {4 n mod 24 | n N } (Note: a mod b is simply the remainder you get when you divide a by b. Thus, 17 mod 7 = 3.) c) {n 3 – 6n 2 + 5n | n {0,1,2,3,4}} 2) For A = {1,2,3,...,14,15}, determine the number of a) the number of subsets of A that contain all of the odd integers in A. b) the number of subsets of A that contain exactly three odd integers. c) the number of 8 element subsets of A that contain exactly three odd integers. d) the number of subsets of A that contain the element 1. e) the number of subsets of A such that the sumof the elements of the subset is less than 6. f) the number of non-empty subsets of A that do not contain the elements 7 and 14. 3) Given that our universe U has 50 elements(|U| = 50) and that A, B and C are sets such that |A| = 25, |B| = 20, |C| = 15, |(A B) C| = 3, |A B| = 8, and |(A B) C| =48, find the following values. Please show your work. (Note: if the values can not be

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