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** **

**Discrete mathematics week 1**

Task Name: Phase 1 Individual Project

Deliverable Length: 2 Parts: See Assignment Details

Details: Weekly tasks or assignments (Individual or Group Projects) will be due by Monday and late submissions will be assigned a late penalty in accordance with the late penalty policy found in the syllabus. NOTE: All submission posting times are based on midnight Central Time.Part I

Part I

Demonstrate DeMorgan’s Laws using a Venn diagram.

• Define two sets representing a group or collection of things that you are familiar with (clearly define the elements or attributes of each set).

• Define also a corresponding Universal set within which the two sets exist.

• State the union and intersection of the two sets and the complements of each set Venn diagrams.

• Using the Venn diagrams for the union of the two sets, the complement of the union of both sets, and the complement of each set, illustrates the DeMorgan’s laws for the example sets that you defined. Note: make sure you create the Venn diagrams, to clearly define the two laws: and .

• Explain each of these two laws using layman’s terms.

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.

Solution Description

DeMorgan’s Laws using a Venn diagram.