We define a dogma as a right-cancellative magma \((D,\star)\) with the property that

\[ (x \star y) \star y = y \star x \qquad \text{for all } x,y \in D. \]

1. Find a dogma of cardinality \(1881\).
2. For which \(n\) does there exist a dogma of cardinality \(n\)?

We define a "dogma" as a right-cancellative magma $(D, \star)$ with the property that $(x \star y) \star y = y \star x$ for all $x, y \in D$.

1. Find a dogma of cardinality $1881$.
2. For which $n$ does there exist a dogma of cardinality $n$?