Difference between revisions of "Subset"
m |
(Started example problem section) |
||
| Line 5: | Line 5: | ||
<math>\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}\}</math> | <math>\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}\}</math> | ||
| + | |||
| + | |||
| + | |||
| + | == Example Problems == | ||
| + | === Intermediate === | ||
| + | * [[1992_AIME_Problems/Problem_2 | 1992 AIME Problem 2]] | ||
Revision as of 19:22, 26 July 2006
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)
