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Math Help - Binary Relations

  1. #1
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    Binary Relations

    Hey all,

    For the following set {a,b,c}, How can I determine if the Relation, R = {(a,a),(a,b),(a,c)} is reflexive, symmetric, antisymmetric or transitive ?

    Thanks.
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  2. #2
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    Quote Originally Posted by Oiler View Post
    Hey all,

    For the following set {a,b,c}, How can I determine if the Relation, R = {(a,a),(a,b),(a,c)} is reflexive, symmetric, antisymmetric or transitive ?

    Thanks.
    Reflexive: For all x we require that x~x

    Symmetric: For all x, y that satisfy x~y, that also y~x

    Antisymmetric: For all x, y if x~y and y~x then x = y

    Transitive: For all x, y, z if x~y and y~z then x~z

    In your case, for example, we know that your relation is not reflexive because there is only one element such that x~x. (ie. a~a, but not b~b and c~c.)

    -Dan
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  3. #3
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    For the case where it is transitive, would you say: a~b and b~c then a~c, but there's no such b~c so the relation is not transitive ?
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