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Set Theory: Drawing Venn Diagrams




 

Sometimes you may be given the description of some sets and you are asked to draw a Venn diagram to illustrate the sets.

First, we need to determine the relationships between the sets such as subsets and intersections. There could be several ways to describe the relationships.

We would draw A within B if we know that:

All members of A belongs to B or A B or A B = B or AB = A

or n(AB) = n(A)

We would draw A overlap B if we know that:

Some members of A belongs to B or AB ≠ Ø or n(A B ) ≠ 0

We would draw disjoint sets A and B if we know that

No members of A belongs to B or A B = Ø or n(A B ) = 0

Example:

U = the set of triangles, I = the set of isosceles triangles,

Q = the set of equilateral triangles and R = the set of right-angled triangles.

Draw a Venn diagram to illustrate these sets.

Solution:

First, we determine the relationships between the sets.

All equilateral triangles are isosceles, so QI. (within)

Some right-angled triangles may be isosceles. RI ≠ Ø (overlap)

Right-angled triangles can never be equilateral. R Q = Ø (disjoint)

Then we draw the Venn diagram:




The following videos show how to use the Venn Diagram to represent set operations for example intersection, union and complement. Venn Diagrams, Unions, and Intersections
Venn diagrams are an important tool allowing relations between sets to be visualized graphically. This chapter introduces the use of Venn diagrams to visualize intersections and unions of sets, as well as subsets and supersets.


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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