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Math Help - Functions - Discrete Math

  1. #1
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    Functions - Discrete Math

    Hello;

    I am looking for an explanation/guidance on how functions work. Here is what I have:

    1.) Determine whethr each of the following relations is a function with domain {1,2,3,4}. For any relation that is not a function, explain why it isn't.

    a.) f={1,1), (2,1), (3,1), (4,1), (3,3)}. - The answer in back of the book states the following: "Not a function; f contains two different pairs of the form (3,-)." What does the dash mean?
    b.) f={(1,2), (2,3), (4,2)} - ?
    d.) f={(1,1), (1,2), (1,3), (1,4) - ?
    e.) f={(1,4), (2,3), (3,2), (4,1)} - ?
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  2. #2
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    Re: Functions - Discrete Math

    Quote Originally Posted by rtrumpow View Post
    Here is what I have: 1.) Determine whethr each of the following relations is a function with domain {1,2,3,4}. For any relation that is not a function, explain why it isn't.
    a.) f={1,1), (2,1), (3,1), (4,1), (3,3)}. - The answer in back of the book states the following: "Not a function; f contains two different pairs of the form (3,-)." What does the dash mean?
    b.) f={(1,2), (2,3), (4,2)} - ?
    d.) f={(1,1), (1,2), (1,3), (1,4) - ?
    e.) f={(1,4), (2,3), (3,2), (4,1)} - ?
    By definition a relation on a set is a function if:
    1) Every element in the set in the first tern some pair in the relation.
    2) No two pairs have the same first term.

    Now in (a) #2 is violated. HOW?

    Now in (b) #1 is violated. HOW?

    Please answer and complete,
    Last edited by Plato; March 18th 2013 at 10:06 AM.
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  3. #3
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    Re: Functions - Discrete Math

    #2 is in violation because of being the first term in two separate pairs.
    #1 contains the same violation.
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  4. #4
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    Re: Functions - Discrete Math

    Quote Originally Posted by rtrumpow View Post
    #2 is in violation because of being the first term in two separate pairs. CORRECT!
    #1 contains the same violation. INCORRECT
    That is one out two.
    What about the parts c) & d) ?
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