Math 301 Name:

Quiz 9

  1. For each of the following, either give an example that fits the requirements or explain why no example is possible.

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    1. A set $A$and a relation on $A$that is symmetric but not reflexive.

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    2. A pair of sets $A,B$and a function $f:Arightarrow B$that is neither one-to-one nor onto.

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    3. A counterexample to the statement MATH

       

       

       

       

    4. Four integers MATHsuch that $q_{1}neq q_{2},$$r_{1}neq r_{2},$$0leq r_{1}<5,$$0leq r_{2}<5,$$22=5q_{1}+r_{1},$and $22=5q_{2}+r_{2}.$

     

     

     


  2. Find each of the following:

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    1. $34func{mod}5$

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    2.     $f^{-1}(2)$where $f:Rrightarrow R$is given by $f(x)=4x-3.$

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    3. The equivalence class $left[ 3right] $for the equivalence relation

MATH