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Math Help - Less than Relation

  1. #1
    Member oldguynewstudent's Avatar
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    Less than Relation

    The less-than relation on [4] is the set
    R={(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)}

    In other words, (a,b) \in R if and only if a < b. It contains six ordered pairs.

    How many ordered pairs are in the less-than relation on [n]?

    How many are in the less-than-or-equal-to relation on [n]?

    The answer to the first question is \sum_{i=1}^{n-1}i or \left({n\atop 2}\right).

    I come up with the following for the second quesiton \sum_{i=1}^{n}i or \left({{n+1}\atop 2}\right). Correct?
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  2. #2
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    Yes, that is correct.
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  3. #3
    Member oldguynewstudent's Avatar
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    Quote Originally Posted by Plato View Post
    Yes, that is correct.
    Thanks for all your help. I realize my hillbilly math is a little crude sometimes, but I'll try to clean it up after my classes start and I have access to my professor.
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