= Solution
In <first-order logic> with equality, the three <first-order sentences> are
$$
\boxed{\begin{aligned}
\text{reflexivity: }&\forall x\,R(x,x),\\
\text{antisymmetry: }&\forall x\forall y\,((R(x,y)\land R(y,x))\to x=y),\\
\text{transitivity: }&\forall x\forall y\forall z\,((R(x,y)\land R(y,z))\to R(x,z)).
\end{aligned}}
$$
A <reflexive relation> relates each element to itself. An <antisymmetric relation> forbids distinct elements from relating in both directions. A <transitive relation> contains every composite of two successive related pairs. Together these axioms define a <partially ordered set>.
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