SO let's say x and y are in relation. Is (x,y) a tuple and an instance of a relation ?
Is a n-tuple an instance of a n-relation?
2025-01-13 06:32:46.1736749966
Can a tuple be defined as an instance of a relationship?
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If $A$ and $B$ are two sets then a relation $R$ is a subset of $A\times B$ where by $A\times B$ we mean the cartesian product of $A$ and $B$. We interpret $(a,b)\in R$ as meaning "$a,b$ are related". So an ordered pair in $R$ is an instance of the relation.
If we have $n$ sets $A_1,\dots,A_n$ then we may define a subset $R$ of $A_1\times\cdots\times A_n$ to be an $n$-ary relation. (Of course for $n=2$ we refer to the $2$-ary relation as simply a relation). We interpret $(a_1,\dots,a_n)\in R$ as "$a_1,\dots,a_n$ are related". So an $n$-tuple in $R$ is an instance of the $n$-ary relation.