Assignment 10

Assignment 10 - Homework 10 -Section 4.4-5c) cfw_s,z 6a)...

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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
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This note was uploaded on 03/18/2012 for the course MAT 108 taught by Professor Staff during the Winter '10 term at UC Davis.

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Assignment 10 - Homework 10 -Section 4.4-5c) cfw_s,z 6a)...

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