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Sets and Logic

by: Meta Gutmann

Sets and Logic MATH 260

Meta Gutmann
GPA 3.81

Jonathon Fassett

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About this Document

Jonathon Fassett
Class Notes
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This 1 page Class Notes was uploaded by Meta Gutmann on Monday October 5, 2015. The Class Notes belongs to MATH 260 at Central Washington University taught by Jonathon Fassett in Fall. Since its upload, it has received 8 views. For similar materials see /class/218976/math-260-central-washington-university in Mathematics (M) at Central Washington University.


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Date Created: 10/05/15
Math 260 Fall 2009 103009 Let f X aY and AB gX Consider the proof ofthe following claim fA B fA fB Proof Let fX Y and ABgX We prove fA BfA fB by proving fA BltfA fB and fA fBfA B Let y e f A 13 By definition of the image of a set there exists an x 6 A03 such that fxy Since xeA B xeA and x63 Itfollows that yfxefA and y fx fB Thus y fx fA fB ShOWing fA B Q fA rUTE Let y e f Ar f B By definition of the image of a set there exists an x E A and x E B such that fx y Since x E A and x E B x E A B It follows that y fx EfA NB showing that fA fB gfA B 1 Find a counterexample showing that the claim is not true N Find the error in the proof and determine what extra condition must be placed on the function f so that the proof can be fixed LA Fix the proof assuming the extra condition in 2 Let fXaY and CDgY Prove or disprove the following 1 f391CUD f391CUf391D 2 f 1CrD f 1C f 1D 3 f 1C D f 1C f 1D


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