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Assignment 10

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

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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 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

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