Demonstrate DeMorgans Laws using a Venn diagram, algebra homework help

Demonstrate DeMorgan’s Laws using a Venn diagram.

1. Draw a Venn diagram showing the elements of sets A, B, and the universe for all 4 regions.
2. Draw a second diagram showing only the elements of the complement of set A.
3. Draw a third diagram showing only the elements of the complement of set B.
4. Draw a fourth diagram showing the union of steps 2 and 3 for the first DeMorgan's law or the intersection of steps 2 and 3 for the second DeMorgan's law.
5. Draw a fifth diagram showing the elements of the intersection of sets A and B for the first DeMorgan's law or the union of sets A and B for the second DeMorgan's law.
6. Finally, draw the last diagram showing the complement of step 5. Compare the results from step 4 against those in step 6 to prove both DeMorgan's laws. In the absence of data elements, you can use 4 different colors to clearly indicate the regions of the universe and follow all of the steps.

Part II

Define two propositions (simple statements that can be either true or false). Give a real-world example of 2 propositions that r and s can represent. Call them r and s. Create a truth table that shows all values of the following:

Proposition

Definition

Your example explained

r

s

¬ r

¬s

r ∧ s

¬ r v s

r ∧ ¬s

Interpret the columns of the truth table for those proposition examples. Interpret the operations on the propositions and the values in the table based on the operations and the values of r and s. Note from Teacher:

Hello Students,

I have had a couple of questions about Unit 1 IP so I thought it would be a good idea to share them with everyone.

For Part I, you should define 2 sets and a universal set within which the 2 sets exist. You should state the union and intersection of the 2 sets, and the complements of each set. Use a Venn diagram to help demonstrate DeMorgan’s laws (both of them) for the sets. For example, set A could be the set of numbers {1,4,9}, and set B could be the set of numbers {1,3,5,7,9}.

Here are two videos that illustrates DeMorgan’s Laws:

https://youtu.be/oOx7FSzSav4

https://www.youtube.com/watch?v=2qCDKt23jHQ

For Part II, you need to define 2 propositions and then fill in the truth table. A proposition is a declarative statement that is either true or false. For example, a proposition for r could be “I like math". The negation of r would be “I do not like math”.