INFS3450 – C&IS – RMU

Venn Diagrams

Here is an example of a Venn Diagram for two sets A and B: 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 Ç 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 È 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) Ù (B U) Ù(C U))

All individuals that are members of one or more of these sets are represented by the labels a…i

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 Î A           T  F  N
2. 2. a Ì A           T  F  N
3. {a, b, f} = A    T  F  N
4. A Ç B = {b, f}            T  F  N
5. C - {d, e} = A È B - C         T  F  N
6. C Ì U              T  F  N
7. C Ë 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 È B È C) =
4. A - {f} =
5. C - {h} =
6. {x| x Î U Ù (x Ï A)} =
7. {x| (x Î A) Ù (x Î C) Ù (x Ï 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