Easy# Subset of a Set: Definition and Identification of Subsets

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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**?