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 $A$ 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)


Example Problems

Intermediate