Definition 3.1.15 (Subsets). Let \(A,B\) be sets. We say that \(A\) is a subset of \(B\), denoted \(A\subseteq B\), iff every every element of \(A\) is also an element of \(B\), i.e. $$ \text{For any object }x,~~x\in A\implies x\in B. $$ We say that \(A\) is a proper subset of \(B\), denoted \(A\subsetneq B\), if \(A\subseteq B\) and \(A\neq B\).
Definition 3.1.15
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Exercise 3.4.3
\(\equiv\) { Definition 3.1.15 }
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Exercise 3.4.2
\(\equiv\) { Definition 3.1.15 }