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
The complement of a union is the intersection of the
The complement of an intersection is the union of the
Draw intersecting circles to represent
the different categories (sets) in the survey.
Next, try to determine the number of elements in the
intersection of all of the sets.
Fill in the other inner portions.
Work from the inner portions to the outer portions,
being sure to subtract the numbers in the portions already
accounted for; move systematically from one region to
Finally, answer the questions asked by reading from
the Venn diagram.