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Math Help - binary relations help please :)

  1. #1
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    binary relations help please :)

    can someone please help me solve these:

    consider a set S of all students, taking some courses chosen from a set of C courses: what are the binary relations?

    R1= (S1,S2) : S1 and S2 take all the same courses together
    R2=(S1,S2) : s1 and S2 take some courses together

    are either equivalence relations too?

    thanks a lot i would appreciate the help ^_^
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  2. #2
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    Quote Originally Posted by Starlight87 View Post
    consider a set S of all students, taking some courses chosen from a set of C courses: what are the binary relations?
    R1= (S1,S2) : S1 and S2 take all the same courses together
    R2=(S1,S2) : s1 and S2 take some courses together

    are either equivalence relations too?
    Yes one of those is an equivalence relation.
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  3. #3
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    An equivalence relation must have three properties:

    a) xRx for all x in the set. (reflexive property)
    b) If xRy then yRx. (symmetric property)
    c) If xRy and yRz then xRz. (transitive property).

    You might want to take a close look at the transitive property for the relations you give.
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