{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment 10 - Homework 10-Section 4.4-5c cfw_s,z 6a(5/2...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework 10 -------------Section 4.4------------- 5c) {s,z} 6a) (5/2, infinity) -------------Section 5.1------------- 1) Reflexive: For any set A, I:A->A where I is the identity map on A is 1-1 and onto, so A relates to A Symmetric: Suppose A relates to B. Then there is a 1-1 onto function f:A->B. Thus f^(-1):B->A is a 1-1 correspondence Thus B relates to A. Transitive: Suppose f:A->B and g:B->C are 1-1 correspondences. Then gof:A->C is a 1-1 correspondence. Thus A relates to C. 2) Suppose (a,b),(c,d) are elements of AxB and f(a,b) = f(c,d). Then (h(a),g(b)) = (h(c),g(d)), so h(a)=h(c) and g(b)=g(d). Since h,g are 1-1, a = c and b = d. So (a,b)=(c,d). Thus f is 1-1. 3b) Let f: A -> A X {x} be defined by f(a) = (a,x). This is then a function on A, since it is defined for all a elt A and the assignment is a unique tuple in A X {x}. It is 1-1, since if f(a1) = f(a2) we have (a1,x) = (a2,x) and equality of tuples requires a1 = a2. It is onto, since if we pick an arbitrary element of the codomain, say (a1, x), we know that a1 maps to it. 4. This is the equation of the straight line from (a,c) to (b,d) (see the graph on p. 208). You need to show that it is
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern