Subset

We say a set is a subset of another set if every element of is also an element of , 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 emphasizes that may be equal to , while says that is any subset of other than 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 is called the power set of and is denoted or .

Example Problems

Introductory

• Counting the number of subsets in a set

Intermediate

• 1992 AIME Problem 2