# Set notation, basic question

• December 6th 2010, 08:39 PM
leoemil
Set notation, basic question
Hi guys,

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

$
x_{ap} \leq 1 \quad \forall a \in A, \forall p \in P
$

and

$
x_{ap} \leq 1 \quad \forall ap \in (A \times P)
$

I am not sure if i can distinguish.

Thanks
• December 6th 2010, 08:45 PM
topspin1617
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.