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If I have a set $A = \{1,2,3,4\}$ why does the Cartesian product of $A \times A$ not include $(2,3) (2.1) (3,1) (3,2) (3,3) or (4,1)(4,2)(4,3)(4,4)$ if its relation subset $R = \{(a,b) : a|b\}$.

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up vote 3 down vote accepted

You are confusing two things here. The Cartesian product $A\times A$ certainly contains pairs such as $(3,2)$ as members. But the relation $R$ (“divides”) does not, because $3\nmid 2$. $(4,4)$ is definitely a member of $R$, though.

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Does 2 divides 3??? Does 2 divides 1??? does 3 divides 1 ???

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