Let $A$ and $B$ be two sets.
We say that $A$ is a subset of $B$, written $A\subseteq B$, if $x\in A$ implies $x\in B$.
If $A$ is not a subset of $B$, we write $A\not\subseteq B$.
If $A\subseteq B$ and there are elements of $B$ that are not in $A$, we sometimes write $A\subset B$.
We denote the empty set (the set with no elements) by $\emptyset$.
Two sets $A$, and $B$ are equal, written $A=B$, if and only if they contain the same elements. We write $A\not=B$ if they are not equal.
Which of the following is false?