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Thread: Elementary Question about Relations

  1. #1
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    Elementary Question about Relations

    I haven't done relations for a while, so when I went back to my textbook to 're-learn' what they were I got slightly confused.

    It says a relation on A is defined of subsets of AxA.

    I then go to the definition of reflexive, which says R is reflexive on A iff for all X that is an element of A, xRx.

    Ok consider A = {x,y}

    Then are the following different relations reflexive? I don't see why not

    R1=(x,x)
    R2=(y,y)
    R3=(y,y) (x,x)
    R4=(y,y) (x,x) (x,y)
    R5=(y,y) (x,x) (y,x)
    R6=(y,y) (x,x) (y,x) (y,x)

    So when it says all a such that (a,a) is in R to be reflexive, does it mean all A in the relation, or all A in the initial set? Thanks
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  2. #2
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    A relation is reflexive if and only if every element in the set is related to itself.
    R1 is not because there is no (y,y).
    R2 is not because there is no (x,x).
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