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Math Help - What is the reflexive closure of R?

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    What is the reflexive closure of R?

    Let R be the relation {(a,b) | a (is not equal to) b} on the set of integers. What is the reflexive closure of R?
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    Re: What is the reflexive closure of R?

    Do you know what these words mean? A relation is "reflexive" if, for every "a" in the set, it is true that aRa. The "reflexive closure" of a relation is the smallest set of pairs, containing the given relation that is reflexive. Here aRb as long as a is not equal to b. What do you get if you add nRn for every integer n to this set?
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    Re: What is the reflexive closure of R?

    Quote Originally Posted by HallsofIvy View Post
    Do you know what these words mean? A relation is "reflexive" if, for every "a" in the set, it is true that aRa. The "reflexive closure" of a relation is the smallest set of pairs, containing the given relation that is reflexive. Here aRb as long as a is not equal to b. What do you get if you add nRn for every integer n to this set?
    Every ordered pair?
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    Re: What is the reflexive closure of R?

    Yes. A reflexive relation contains all pairs of the form "(a, a)". This relation, as given, contains all other pairs so the "reflexive closure" of this relation is the set of all ordered pairs of integers.
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