LOGIC

FINAL

EXAM

 

 

 

 

 

PART 1: Diagramming (10 points)

Instructions: Using the numbering scheme provided, construct a diagram of the arguments in the passage below.

1 Cox Communications should compensate my uncle Smedley. 2 The lights from the SDSU/Cox billboard are very bright, and because of this the billboard keeps people who live across the street from it awake at night. 3 Those people who live across the street from the billboard are therefore inconvenienced by it. 4 Any billboard that contains the logo of a business acts as an advertisement for that business. 5 The SDSU/Cox billboard contains the logo of Cox Communications. 6 Cox Communications is a business. So 7 the SDSU/Cox billboard acts as an advertisement for Cox Communications. 8 If the SDSU/Cox billboard inconveniences people who live across the street from it and it acts as an advertisement for Cox Communications, then Cox Communications should compensate those people for the inconvenience they suffer. Hence, 9 Cox Communications should compensate the people who live across the street from the billboard and are inconvenienced by it. 10 My uncle Smedley lives across the street from the billboard.

 

PART 2: Translation (15 points)

Instructions: Using the translation key provided, translate the statements below into symbolic notation.

Translation Key

A: Cox Communications administrators love Las Vegas.

B: SDSU administrators love Las Vegas.

C: Cox administrators live across the street from the SDSU/Cox Communications billboard.

D: SDSU administrators live across the street from the SDSU/Cox Communications billboard.

F: The SDSU/Cox Communications billboard flashes messages all night long.

L: Uncle Smedley lives across the street from the SDSU/Cox Communications billboard.

U: Uncle Smedley goes crazy.

A. If either Cox or SDSU administrators live across the street from the SDSU/Cox Communications billboard they must love Las Vegas.
B. The SDSU/Cox Communications billboard flashes messages all night long if and only if neither Cox nor SDSU administrators live across the street from it.
C. Uncle Smedley goes crazy provided that he lives across the street from the SDSU/Cox Communications billboard and the billboard flashes messages all night long.

PART 3: Truth Table (15 points)

Instructions: Determine whether the statement below is logically true, logically false, or logically indeterminate by constructing a truth table.

- ( - (P = - Q) v - ( - R > (P . - Q)))

PART 4: Consistency Tree (15 points)

Instructions: Determine whether the set of statements below is consistent or inconsistent by constructing a consistency tree.

{ ( P > - Q) ; ( - P v Q) ; (P v (R v S)) ; ((R > T) . (S > T)) ; - T }

PART 5: Proof (15 points)

Instructions: Construct a proof of the following argument.

( - P v - Q)

(P > Q)

(P v (R v S))

((R > T) . (S > T))

__________________

(T v M)

PART 6: Syllogism (15 points)

Instructions: Identify the mood and figure of the argument below. Explain whether the argument is valid or invalid on both the Classical Theory and on the Modern Theory. If it is invalid on either of the theories, identify the rule (or rules) it violates.

Since some educational institutions are organizations owned and operated by Cox Communications, but no organizations owned and operated by Cox Communications are organizations whose actions ever conflict with the interests of Cox Communications, it follows that some educational institutions are not organizations whose actions ever conflict with the interests of Cox Communications.

PART 7: Venn Diagram (15 points)

Instructions: Construct two Venn diagrams on the argument in Part 6, one from the modern perspective, the other from the classical perspective. Label the two diagrams ‘Modern’ and ‘Classical’, and identify the three rectangles in each diagram.