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Math Help - Set notation, basic question

  1. #1
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    Set notation, basic question

    Hi guys,

    Sat i have two set A = {1,2}, P = {1,2,3}, are the two formulations below equivalent:

    <br />
x_{ap} \leq 1 \quad \forall a \in A, \forall p \in P<br />

    and

    <br />
x_{ap} \leq 1 \quad \forall ap \in (A \times P)<br />

    I am not sure if i can distinguish.

    Thanks
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  2. #2
    Member
    Joined
    Nov 2010
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    Yes, the two conditions
    \forall \, a\in A, \, \forall \, p\in P and

    \forall \, (a,p)\in A\times P

    are equivalent. Taking an arbitrary pair, one from A and one from P, is the same as choosing any element from A and any element from P.
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