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**Test Yourself**

1. If $R$ is a relation from $A$ to $B$, $x \in A$, and $y \in B$, the notation
   $x R y$ means that ____.

$x$ is related to $y$ by $R$

2. If $R$ is a relation from $A$ to $B$, $x \in A$, and $y \in B$, the notation
   $x \cancel{R} y$ means that ____.

$x$ is not related to $y$ by $R$.

3. If $R$ is a relation from $A$ to $B$, $x \in A$, and $y \in B$, the notation
   $(y, x) \in R^{-1}$ if, and only if, ____.

$$ (x, y) \in R $$

4. A relation on a set $A$ is a relation from ____ to ____.

$A$; $A$

5. If $R$ is a relation on a set $A$, the directed graph of $R$ has an arrow
   from $x$ to $y$ if, and only if, ____.

$x$ is related to $y$ by $R$