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Math Help - Determine whether the following relation is transitive

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    Determine whether the following relation is transitive

    Q) Determine whether the following relation is transitive
    Relation R in the set N of natural numbers defined as
    R = { (x,y) : y=x+5 and x<4}
    The text book says that it is transitive. I dd not understand how it is transitive. Please help.
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    Quote Originally Posted by myth31 View Post
    Q) Determine whether the following relation is transitive
    Relation R in the set N of natural numbers defined as
    R = { (x,y) : y=x+5 and x<4}
    The text book says that it is transitive. I dd not understand how it is transitive. Please help.
    This is a trick question in that the relation  \mathcal{R} is vacuously transitive.
    If (a,b)\in \mathcal{R} then b=a+5 which implies that b\ge 5.
    So that means that \left( {\forall c \in \mathbb{N}} \right)\left[ {(b,c) \notin \mathcal{R}} \right]
    So the relation is transitive by default.
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