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Considering binary relationships, possible cardinality ratios are:

1. one:one
2. $1:N$
3. $M:N$
4. All the options

A binary relation is not a binary operation (groups, monoids).

A binary relation on X and Y, is simply a subset of $X \times Y$.

A binary operation on X is a mapping from $X \times X \rightarrow X$.

So any of the first 3 options are possible.
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