Properties: N/A
Sufficiencies: N/A
Questions: N/A

Subset

Given two sets $A$ and $B$ , we say $A$ is a subset of $B$ if and only if every element of $A$ is also an element of $B$ , written

A \subseteq B .

If there is an element of $A$ not contained in $B$ , then we say $A$ is not a subset of $B$ and we write

A ⊈ B .

Visual Representation

300

⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠

A
B
A
B

⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠

A
B
A
B

\begin{proof}
Suppose $x \in A$ .
$⋮$ <-- work of math!
Therefore $x \in B$ .
By definition $A \subseteq B$ .
\end{proof}