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Heather M. Stephens
Math 215-1303A-01Instructor: Jeremy Bolton7/15/2013
Individual Project 1 |

1) Define two sets: (7 points)
∆ = AND
Ů = OR
ⁿ = NOT
Skate Board Brands = {Sizes}
Blind = {7, 7.5, 7.75, 8}
Element = {7, 7.25, 7.75, 8.25}
Union = B ∆ E {7, 7.5, 7.75, 8, 7.25, 8.25}
Intersection = B Ů E ={7, 7.75}
Non Disjoint = B ∆ E

2) Define the Universal set that contains the two sets you created above. View the live chat or archives: (7 points)

Skate board brands and their sizes. Set 1 is Blind with sizes 7, 7.5, 7.75, and 8. Set 2 is Element with sizes 7, 7.25, 7.75, and 8.25.

3) State the union of the two sets you have defined above. (6 points)

Union of B ∆ E = {7, 7.25, 7.5, 7.75, 8, 8.25}

4) State the intersection of the two sets you have defined above: (6 points)

Intersection of B Ů E = {7, 7.75}

5) State the complements of each set of the two sets you defined above: (6 points)

Set A = {7.25, 8.25} = what is NOT Blind but is Element = ⁿB∆E Set B = {7.5, 8} = what is Blind but NOT Element = B∆ⁿE

6) Illustrate both of DeMorgan’s Laws using Venn diagrams you will have separate Venn Diagrams for each Law.
Law 1:
ⁿ(B∆E) = (ⁿB) Ů (ⁿE)
B∆E
B∆E

Law 2:
B∆E
B∆E
ⁿ(BŮE) = (ⁿB) ∆ (ⁿE)

7) Explain each of the two DeMorgan’s laws using layman’s terms: (6 points)

ⁿ(B∆E) = (ⁿB) Ů (ⁿE) = NOT (Blind AND Element) = (NOT Blind) OR (NOT Element)

It means Not Blind AND NOT Element =It means Not Blind OR Element

ⁿ(BŮE) = (ⁿB) ∆ (ⁿE) = NOT (Blind OR Element) = (NOT Blind) AND (NOT Element)

It means Not Blind OR Element = It means Not Blind AND NOT Element

Part 2: (see hint below) (50 points total)

Proposition | Truth Values Definitions | Your example explained | r | T | T | F | F | r: it is raining | s | T | F | T | F | s: it is cold | ¬ r | F | F | T | T | It’s NOT raining | ¬s | F | T | F | F | It’s Not cold | r ∧ s | T ∆ T | T ∆ F | F ∆ T | F ∆ F | It’s raining and it’s cold | ¬ r v s | ⁿF Ů T | ⁿF Ů F | ⁿT Ů T | ⁿT Ů F | It’s not raining and it’s cold | r ∧ ¬s | T ∆ ⁿF | T ∆ ⁿT | F ∆ ⁿF | F ∆ ⁿF | it is raining AND it is not cold |