In Class Activity
MAT 300, Spring 2006
January 31, 2006
Imagine three sets A, B, C that have non-empty intersections. This is the same setting as
the enrollment problem.
1. Draw a Venn diagram to illustrate this setting, labeling each of the large circles with
A, B or C.
2. Now label each space on the Venn diagram, using the sets A, B, C and connector
such as intersection, union, compliment or set difference.
3. Try to label as many of the sets as possible with more than one label.
4. Pick a space where you have two descriptions for the same space. Try to prove that
those two ways of describing the space are equivalent.
5. Would your two expressions from 4 always be equivalent for any sets A, B, C? Does
it matter whether or not A is a subset of B or if B and C are disjoint?
Here are some informal notes from our book about two other useful sets:
• The difference A\B is the set of all elements in A that are not in B.
• The symmetric difference A∆B is the set of elements that are either in A or B, but not
both.
Find two ways of writing each of these sets in terms of compliments, intersections and
unions.
