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Demonstrate DeMorgan’s Laws using a Venn diagram.
- Draw a Venn diagram showing the elements of sets A, B, and the universe for all 4 regions.
- Draw a second diagram showing only the elements of the complement of set A.
- Draw a third diagram showing only the elements of the complement of set B.
- 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.
- 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.
- 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.
Define two propositions (simple statements that can be either true or false). Give a real-world example of 2
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