Subset

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We say a set $A$ is a subset of another set $B$ if every element of $A$ is also an element of $B$, and we denote this by $A \sub B$ (Error compiling LaTeX. Unknown error_msg). The empty set is a subset of every set, and every set is a subset of itself. The notation $A \subseteq B$ emphasizes that $A$ may be equal to $B$, while $\displaystyle A \subsetneq B$ says that $A$ is any subset of $B$ other than $B$ itself.


The following is a true statement:

$\emptyset \sub \{1, 2\} \sub \mathbb{N} \sub \mathbb{Z} \sub \mathbb{Q} \sub \mathbb{R} \sub \mathbb{C} \sub \mathbb{C}\, \cup\{\textrm{Groucho, Harpo, Chico}\} \supset \{1, 2, i, \textrm{Groucho}\}$ (Error compiling LaTeX. Unknown error_msg)


The set of all subsets of a given set $S$ is called the power set of $S$ and is denoted $\mathcal{P}(S)$ or $2^S$.

Example Problems

Introductory

Intermediate