Explanation:
Venn diagram
Venn diagram showing the intersections of the Greek, Latin and
Russian alphabet (upper case graphemes)
Venn diagrams or set
diagrams are diagrams that show all possible logical relations
between a finite collection of sets (aggregation of things). Venn diagrams were conceived around 1880 by John
Venn. They are used to teach elementary set
theory, as well as illustrate simple set relationships in probability, logic, statistics, linguistics and computer
science
Overview
A Venn diagram is constructed with a collection of simple closed
curves drawn in a plane.
Venn diagrams normally comprise overlapping circles.
The interior of the circle symbolically represents the elements of
the set, while the exterior represents elements which are not members of the
set.
(Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Venn_diagram
Basic
operations
There are several fundamental operations for constructing new sets
from given sets.
Unions
The union of A and B,
denoted A ∪ B
Two sets can be "added"
together. The union of A and B,
denoted by A ∪ B, is the
set of all things which are members of either A or B.
Examples:
1. {1,
2} ∪ {red, white} = {1, 2, red, white}.
2. {1,
2, green} ∪ {red, white, green} = {1, 2, red, white, green}.
3. {1,
2} ∪ {1, 2} = {1, 2}.
(Our solved example in mathguru.com uses
this concept)
Some basic properties of unions:
1. A ∪ B = B ∪ A.
2. A ∪ (B ∪ C) = (A ∪ B) ∪ C.
3. A ⊆ (A ∪ B).
4. A ∪ A = A.
5. A ∪ ∅ = A.
6.
A ⊆ B if
and only if A ∪ B = B.
Intersections
A new set can also be constructed by determining which members
two sets have "in common". The intersection of A and B,
denoted by A ∩ B, is the set of all things which are
members of both A and B.
If A ∩ B = ∅, then A and B are said to be disjoint.
The intersection of A and B,
denoted A ∩ B.
Examples:
1. {1,
2} ∩ {red, white} = ∅.
2. {1,
2, green} ∩ {red, white, green} = {green}.
3. {1,
2} ∩ {1, 2} = {1, 2}.
(Our solved example in mathguru.com uses
this concept)
Some basic properties of intersections:
- A ∩ B = B ∩ A.
- A ∩ (B ∩ C) = (A ∩ B) ∩ C.
- A ∩ B ⊆ A.
- A ∩ A = A.
- A ∩ ∅ = ∅.
•
A ⊆ B if and
only if A ∩ B = A.
http://en.wikipedia.org/wiki/Set_(mathematics)
The
above explanation is copied from Wikipedia, the free encyclopedia and is
remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported
License.