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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 11 and onto, so A relates to A
Symmetric: Suppose A relates to B.
Then there is a 11 onto
function f:A>B.
Thus f^(1):B>A is a 11 correspondence
Thus B relates to A.
Transitive: Suppose f:A>B and g:B>C are 11 correspondences.
Then gof:A>C is a 11 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 11, a = c and b = d.
So (a,b)=(c,d).
Thus f is 11.
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 11, 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.
 Winter '10
 Staff

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