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Math 221 Homework 1

# Math 221 Homework 1 - Math 221 Week 1 Exercises Directions...

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Unformatted text preview: Math 221 Week 1 Exercises Directions: Work through these exercises, and be prepared to discuss them in class on Friday. There will be a quiz on Monday based on this material. 1. In each of the parts, you are given an explicit list representation for a ﬁnite set A. Please give a universal set U , and a predicate P , so that A = {x ∈ U : P (x) = true}. (b) A = {MATH 220, CS 270, ECE 200} Hint: Math course descriptions (with prerequisites) can be found at http://duapp1.drexel.edu/webcourses/ 2. In each of the following parts (a-f) you are given a ﬁnite set A that is speciﬁed using a predicate P (x) on a universal set U . Please ﬁnd an explicit list representation for the set. The ﬁrst two are are done for you so that it is clear what is being asked. (a) U = N, A = {x ∈ U : x ≤ 6 and x is even} Answer: {0, 2, 4, 6}. (a) A = {0, 1, 2} (b) U = P owerset({a, b, c}), A = {x ∈ U : a ∈ x}. ￿ ￿ Answer: A = {a}, {a, b}, {a, c}, {a, b, c} (d) U = R, A = {x ∈ U : x2 − 5x + 6 = 0}. (c) U = Z+ , A = {x ∈ U : x ≤ 6 and x is even} 3. There are 9 functions that have domain {1, 2} and codomain {a, b, c}. x f(x) a . List the other 8 functions. For each of the 9 One of them is 1 2 b functions, decide whether it is 1-1 and whether it is onto. 4. There are 8 functions that have domain {a, b, c} and codomain {1, 2}. x f(x) a 1 One of them is . List the other 7 functions. For each of the 8 b 1 c 1 functions, decide whether it is 1-1 and whether it is onto. 5. Textbook problems: Ch.1, numbers 1,2,15,19. 6. Suppose U = {1, 2, 3, 4, 5} is the universal set. Let A = {1, 2}, and let B = {2, 3, 4}. In each of the following parts, a set is deﬁned using set operations. Give an explicit list representation for the set. (a) A ∩ B = 1 (b) A ∪ B = (d) A − B = (e) A ∩ B = (f) B ∩ B = (c) A ∪ A = (g) A ∪ B = 7. Let A = {a, b} and let B = {1, 2, 3}. (b) What is the cardinality of B × A × B ? (a) Give explicit list representations for A × A and A × B 2 ...
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