109_sp2011_ho_injsurj_sol

109_sp2011_ho_injsurj_sol - 109 Spring 2011 - Injections...

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109 Spring 2011 - Injections and Surjections Exercise (II.12) . Suppose that A Z . Write the following statement entirely in symbols using the quantiFers and . Write out the negative of this statement in symbols. There is a greatest number in the set A . Give an example of a set A for which this statement is true. Give an example of a set A for which it is false. a A x A ( x a ) If A = { 1 , 2 , 5 } then the statement is true. If A = Z then the statement is false. Exercise (II.17) . ±unctions f : R R and g : R R are deFned as follows. f ( x )= x +2 if x< 1, x if 1 x 1 x 2i f x> 1; g ( x )= x 2i f x< 1, x if 1 x 1 x +2 if x> 1 ±ind the functions f g , g f .I s g the inverse of f ?I s f injective or surjective? Is g ? f g ( x )= x ; g f ( x )= x if x< 3, ( x +2) if 3 x<
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This note was uploaded on 08/02/2011 for the course MATH 109 taught by Professor Knutson during the Spring '06 term at UCSD.

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109_sp2011_ho_injsurj_sol - 109 Spring 2011 - Injections...

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