Why is the empty set a subset of every set?

In set theory, a set $A$ is defined as a subset of a set $B$ (symbolized as $A\subseteq B$) if every element of $A$ is also an element of $B$.123

The empty set—a set that contains no elements—is considered a subset of every set because it satisfies this definition vacuously. Specifically, because the empty set has no elements, there is no element within it that fails to be a member of any other given set. In logical terms, the statement "for all $x$, if $x$ is a member of the empty set, then $x$ is a member of set $B$" is considered true because the antecedent (the condition that $x$ is a member of the empty set) is always false. Therefore, the condition for subset inclusion is satisfied for any set $B$.13