**left-total binary relation**if and only if \begin{equation} \forall \, X \in X : \exists \, y \in Y : (x, y) \in R \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Total binary relation

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Total binary relation

Formulation 0

A D4: Binary relation $B = (X \times Y, R)$ is a **left-total binary relation** if and only if
\begin{equation}
\forall \, X \in X :
\exists \, y \in Y :
(x, y) \in R
\end{equation}