LOGIC AND PROOF
HOMEWORK 8
1.
Consider the function f: {1,2,3,4,5,6,7}
{0,1,2,3,4,5,6,7,8,9} given as
f{(1,3), (2,8), (3,3), (4,1), (5,2), (6,4), (7,6)}
Find f({1,2,3}) and f
‐
1
({0,5,9}).
2.
Let g:
Գ
x
Գ
Գ
by g(m,n) = 2
m
3
n
, let A = {1,2,3}, and let C = {1,4,6,9,12,16,18}.
Find g(A x A) and g
‐
1
(C).
3.
Prove that the converse of Theorem 4.5.1 (a) is true when f is 1
‐
1.
4.
Provide a counterexample to show that the converse of Theorem 4.5.1 (a) is not true when f is
not 1
‐
1.
5.
Use an epsilon argument to prove that if x
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 Spring '08
 EVINSON
 Calculus, Logic, Xn, epsilon argument

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