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Math Help - Functions and properties

  1. #1
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    Functions and properties

    Hi guys, im am so frustrated right now. I suck at discrete math. I dont understand it at all, the proffesor talks to fast. Im on the vergre of tears. Plus theres no tutoring for this class, and i really need help. right now i have two problems

    1. suppose g: A--->B and f: B---> C are both one to one, prove f (o) g what does the little o mean?) i have no idea how to start this.


    2. if E is an equivalance equation on A , then prove or give an counter example, E (o) E is an equivalnce on A. Im not even sure what this is asking. i dont really get equivalance equations or sets and relations really, all i know is E are transitive, reflexive and symmetric.
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  2. #2
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    Quote Originally Posted by Wardub View Post
    1. suppose g: A--->B and f: B---> C are both one to one, prove f (o) g what does the little o mean?) i have no idea how to start this.
    This notation suggests the succcessive operation of the two functions.

    Start with a value from the Domain of 'g'.
    Map this through 'g' to the range of 'g'.
    This becomes the Domain of some subset of 'f'.
    Map the new value through 'f'.
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  3. #3
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    but there is no value of f or g, what do i do when theres nothing to begin with?
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  4. #4
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    prove f (o) g
    Is this REALLY the problem statement? Doesn't seem like much to go on.
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  5. #5
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    I assume that #1 is, if f:A \mapsto B\quad \& \quad g:B \mapsto C are both one-to-one then so is g \circ f.
    The proof is quite easy:
    \begin{array}{rcl}<br />
 g \circ f(p) & = & g \circ f(q) \\ <br />
 f(p) & = & f(q),\; \mbox{g is 1-1} \\ <br />
 p & = & q,\quad \mbox{f is 1-1} \\ <br />
 \end{array}

    For #2. If R\quad \& \quad S are relations on a set that are reflexive, symmetric and transitive then R \circ S is reflexive, symmetric and transitive.
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