INFS3450 C&IS RMU

Venn Diagrams

 

Here is an example of a Venn Diagram for two sets A and B:

 

image001

 

Here is an example for one set A, showing the complement of A (or non-A) as the area inside the universe and outside the circle representing set A (the universe minus set A).

U - A

 

 

Here is a two-set Venn diagram using shading to show the intersection of two sets.

[Note: non-shaded areas of Venn diagrams are empty; set members that exist may be in the shaded areas.]

 

S P

 

 

 

Here is a two-set Venn diagram using shading to show the union of two sets.

[Note: non-shaded areas of Venn diagrams are empty; set members that exist may be in the shaded areas.]

S P

 

 

 

Venn Diagram applications and examples:

         Sustainable Development: http://en.wikipedia.org/wiki/Portal:Sustainable_development

         Market Survey Sampling: http://www.beva.org/maen503/week2/venn_diagram_examples.htm

         Regents Venn Diagram Examples: http://regentsprep.org/Regents/math/ALGEBRA/AP2/PracVenn.htm

         Shodor Venn Diagrams Shapes: http://www.oerrecommender.org/visits/117929

         TAMU Tournaments Example: http://mpeg.math.tamu.edu/Joe_Kahlig/venn/tournaments.html

         TAMU Pollutants Example: http://www.math.tamu.edu/~kahlig/venn/pollutants/pollutants.html

         TAMU Space TV Shows Example: http://www.math.tamu.edu/~kahlig/venn/trek/trek.html

         TAMU Mexican Restaurant Example: http://www.math.tamu.edu/~kahlig/venn/restaurant/restaurant.html

         TAMU Van Halen Example: http://www.math.tamu.edu/~kahlig/venn/concert/concert.html

         TAMU Mythological Figures Example: http://www.math.tamu.edu/~kahlig/venn/mythology/mythology.html

 

 

Here is a 3-set Venn Diagram, with the individual members identified:

The diagram represents sets A, B, C, and universe U, where ((A U) (B U) (C U))

All individuals that are members of one or more of these sets are represented by the labels ai

For the exercise here using formal logic and set notation, practice reading the formal expressions out loud.

A. We can evaluate these statements in terms of the above Venn Diagram as true (T) or false (F) or not shown (N)

  1. 1. a A T F N
  2. 2. a A T F N
  3. {a, b, f} = A T F N
  4. A B = {b, f} T F N
  5. C - {d, e} = A B - C T F N
  6. C U T F N
  7. C U T F N
  8. |C| > |B| T F N

B. We can evaluate the following statements in terms of the preceding Venn Diagram, using set notation:

  1. [Example] C = {d, e, f, g, h}
  2. C - B =
  3. U - (A B C) =
  4. A - {f} =
  5. C - {h} =
  6. {x| x U (x A)} =
  7. {x| (x A) (x C) (x B)} =

2011 Robert Morris University

Contacts:
Valerie J. H. Powell, RT(R ), PhD, RMU C&IS Department and
E. Gregory Holdan, PhD, RMU Mathematics Education Program