Let n1, n2, . . ., n9 denote the 9 digits of you Student ID. We define the following three subsets of the natural numbers: A = {n1, n2, . ., n9} B = {n1, n2, n3, n4, n5} C = {n6, n7, n8, n9} Let student id be: 001203513 (a) State your student ID and define the above three sets for your ID by listing their elements. What are the sizes of the sets A, B and C? (b) Does there exist a function f from B to C that is one-to-one? If so define one, if not, explain why not. (c) Does there exist a function g from B to C that is onto? If so define one, if not, explain why not. 1 (d) How many elements are there in the set A2 ? (e) As a relation over A, is B \times C reflexive, transitive and symmetric? For each property explain why or why not
Let n1, n2, . . ., n9 denote the 9 digits of you Student ID. We define the following three subsets of the natural numbers: A = {n1, n2, . ., n9} B = {n1, n2, n3, n4, n5} C = {n6, n7, n8, n9} Let student id be: 001203513 (a) State your student ID and define the above three sets for your ID by listing their elements. What are the sizes of the sets A, B and C? (b) Does there exist a function f from B to C that is one-to-one? If so define one, if not, explain why not. (c) Does there exist a function g from B to C that is onto? If so define one, if not, explain why not. 1 (d) How many elements are there in the set A2 ? (e) As a relation over A, is B \times C reflexive, transitive and symmetric? For each property explain why or why not
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 85E
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Transcribed Image Text:Let n1, n2, . . ., n9 denote the 9 digits of you Student ID. We define the following three
subsets of the natural numbers:
A = {n1, n2, . ., n9}
B = {n1, n2, n3, n4, n5}
C = {n6, n7, n8, n9}
Let student id be: 001203513
(a) State your student ID and define the above three sets for your ID by listing their
elements. What are the sizes of the sets A, B and C?
(b) Does there exist a function f from B to C that is one-to-one? If so define one, if
not, explain why not.
(c) Does there exist a function g from B to C that is onto? If so define one, if not,
explain why not.
1
(d) How many elements are there in the set A2
?
(e) As a relation over A, is B \times C reflexive, transitive and symmetric? For each
property explain why or why not
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