% Relations

\instatements{\newpage}

\begin{examproblem}{20}
Relate each of the following relational expressions to the relation
property it describes from the list below.

properties: transitive, reflexive, irreflexive, symmetric, antisymmetric,
asymmetric,

expressions:
$R^2 \subseteq R$ \solution{transitive},\\
$R = R^+$ \solution{transitive},\\
$I_A \subseteq R$ \solution{reflexive},\\
$I_A \intersect R = \emptyset$ \solution{irreflexive},\\
$R^{-1} \subseteq R$ \solution{symmetric},\\
$R^{-1} \intersect R \subseteq I_A $ \solution{antisymmetric}.
\end{examproblem}

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