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is the cardinality of the set {characters in set A}?

is the cardinality of the set {characters in set A}?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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5) What is the cardinality of the set {characters in set A}? 6) Let X = {strings in A}. Find |X 7) Let X {strings in A} Name two B, CC X and two D, ECX such that... a) BUC X B = C = b) DNE #Ø E = 8) Suppose we define a relation on the set {strings in A} by making 69°F a
Transcribed Image Text:5) What is the cardinality of the set {characters in set A}? 6) Let X = {strings in A}. Find |X 7) Let X {strings in A} Name two B, CC X and two D, ECX such that... a) BUC X B = C = b) DNE #Ø E = 8) Suppose we define a relation on the set {strings in A} by making 69°F a
Page く of 2 ZOOM + 8) Suppose we define a relation on the set {strings in A} by making aRb + length(a) = length(b) Support or refute the following statements. Explain your reasoning. a) The relation as defined in 8) is reflexive. b) The relation as defined in 8) is symmetric. c) The relation as defined in is transitive. d) The relation as defined in 8) is an equivalence relation. 9) Suppose we instead define a function on the set {strings in A} by f: {strings of A} → N f(x) = |x| where |x| is the cardinality of the set of characters in that string. Support or refute the following statements. Explain your reasoning. a) The function as defined in 9) is 1-1. b) The function as defined in 9) is onto. c) The function as defined in 9) is reliably invertible. 69°F 10/
Transcribed Image Text:Page く of 2 ZOOM + 8) Suppose we define a relation on the set {strings in A} by making aRb + length(a) = length(b) Support or refute the following statements. Explain your reasoning. a) The relation as defined in 8) is reflexive. b) The relation as defined in 8) is symmetric. c) The relation as defined in is transitive. d) The relation as defined in 8) is an equivalence relation. 9) Suppose we instead define a function on the set {strings in A} by f: {strings of A} → N f(x) = |x| where |x| is the cardinality of the set of characters in that string. Support or refute the following statements. Explain your reasoning. a) The function as defined in 9) is 1-1. b) The function as defined in 9) is onto. c) The function as defined in 9) is reliably invertible. 69°F 10/
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