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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$(2,2),(1,1),(3,3),(4,4)$ are members. – jiten Jan 06 '22 at 07:30
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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.
Harald Hanche-Olsen
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A simple way you could solve this problem would be to list the 16 ordered pairs and then see which ordered pairs fit into the "divides" relation. In this case, a few of the elements you listed do not fit into the relation because for example, 2 does not divide by 3 etc.
