Is the null set a subset of every set? [duplicate]

Ever since day one of of my Mathematical Logic course, this fact has really bothered me. I cannot wrap my head around how an empty set is a subset of every possible set. Could someone kindly explain how this is true? Any help is appreciated!

If you're comfortable with proof by contrapositive, then you may prefer to prove that for any set $A,$ if $x\notin A,$ then $x\notin\emptyset$. But of course, $x\notin\emptyset$ is trivial since $\emptyset$ has no elements at all. Hence, $x\notin A\implies x\notin\emptyset,$ so by contrapositive, $x\in\emptyset\implies x\in A,$ meaning $\emptyset\subseteq A$.

By definition, $A$ is a subset of $B$ if every element of $A$ is in $B$.

If we set $A=\emptyset$, then the above statement is vacuously true. Every element of $A$ is in fact an element of $B$ since the former has no elements.

A remarkably simple way of trying to grasp why that is the case is as follows:

We can consider any set and throw away all its elements, then we are left with the subset { }. This means that { } is a subset of any set.