MATH215-1101B-03 Discrete Mathematics
Phase 1 Individual Project
February 21, 2011
Demonstrate DeMorgan’s Laws using a Venn diagram.
The sections below define 2 sets and a universal set within which the 2 sets exist. They state the union and intersection of the 2 sets and the complements of each set. The Venn Diagrams help demonstrate DeMorgan’s laws for sets.
The Union is the combined elements of both sets A and B. The Union is expressed below and is shown in all shaded areas of the Venn Diagram.
A U B =
De Morgan’s Law
(AUB)’ = A’
Below are the values of r and s. There are seven instances below and each is interpreted by what their values are, followed by a truth table for those examples.
r = I am using the computer
s = I am doing homework
- r = I am using the computer
- s = I am doing homework
- ¬ r = I am not using the computer
- ¬s = I am not doing homework
- r ∧ s = I am using the computer and doing homework
- r ∧ ¬s = I am using the computer, but I am not doing homework.
- ¬ r v s = I am not using the computer, but I am doing homework.