Essential Ideas for Section 2.3

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.