What about the sets \(A = \{1, 2, 3\}\) and \(B = \{1, 2, 3, 4\}\text{?}\) Clearly \(A \ne B\text{,}\) but notice that every element of \(A\) is also an element of \(B\text{.}\) Because of this we say that \(A\) is a subset of \(B\text{,}\) or in symbols \(A \subset B\) or \(A \subseteq B\text{.}\) Both symbols are read “is a subset of.” The difference is that sometimes we want to say that \(A\) is either equal to or is a subset of \(B\text{,}\) in which case we use \(\subseteq\text{.}\) This is analogous to the difference between \(\lt\) and \(\le\text{.}\)
in-context