Operations with Sets
Remember the basic operations (from the last section):
Complement
The complement of a set S is consists of everything that is not in S.
Union
The union of two sets is everything that is in either set; that is, anything colored (blue, yellow, or green).
Intersection
The intersection of two sets is everything that is in both sets; that is, anything
colored both blue and yellow, namely green.
Combined Operations
For combined operations, perform operations in parenthesis first, then proceed from left
to right. To find a complement, first find the set under the overbar, and then shade
all parts not contained under the overbar.
De Morgan's Laws
There are two parts to De Morgan's Law.
The complement of a union is the intersection of the complements.
The complement of an intersection is the union of the complements.
Survey Problems
Draw intersecting circles to represent the different categories (sets) in the
survey.
Next, try to determine the number of elements in the intesection of all of the
sets.
Fill in the other innner portions.
Work from the inner portions to the outer protions, being sure to subtract the
numbers in the portions already accounted for; move systematically from one region
to another.
Finally, answer the questions asked by reading from the Venn diagram.