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**Definition**

Let $R$ be a relation from $A$ to $B$. Define the inverse relation $R^{-1}$ from
$B$ to $A$ as follows:

$$ R^{-1} = \{(y, x) \in B \times A | (x, y) \in R\} $$

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**Definition**

A **relation on a set** A is a relation from $A$ to $A$.

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Page 514

**Definition**

Given sets $A_1, A_2, \dots, A_n$ an **$n$-ary relation** $R$ on
$A_1 \times A_2 \times \cdots \times A_n$ is a subset of
$A_1 \times A_2 \times \cdots \times A_n$. The special cases of $2$-ary,
$3$-ary, and $4$-ary relations are called **binary**, **ternary**, and
**quarternary relations**, respectively.