LOGIC

FINAL
EXAMINATION

PART 1: Diagramming (10 points)

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

¹If Sandy Claws comes in the house through doggie door and Rover’s there our Christmas cat will be no more. ²But there he sits without a whine, without a bark the sentry dog on duty waits in cold and dark. So ³if through pooch’s door our feline friend must go no doubt that night she’ll say “Oh no!” and not “Ho, ho!” as Christmas tight in doggie jaws she quits the cause and finds between all cats and dogs there are no laws. ⁴If Sandy Claws comes in the house through chimney flue that Holy Night our little cat will always rue, for fire bright will not just hearth and mantle light and cause her fright, it will also make her paws ignite. ⁵So if Ms. Claws must either brave the door or flue or else outside at night remain both cold and blue, as you can see, our cat will be in heaven’s jaws or Sandy Claws will walk henceforth with hellish paws. But ⁶no dog or cat on Christmas day gets great gifts galore unless it gets inside the house through flue or door. So ⁷our cat will either be extremely poor, or dead, or else, you see her paws will be flamed brightly red.

PART 2: Translation (15 points)

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

Translation Key:

D: Sandy Claws comes in through doggie’s door.
F: Sandy Claws comes in through chimney flue.
G: Sandy Claws gets gifts galore.
J: Sandy Claws gets caught in pooch jaws.
M: Sandy Claws exists no more.

A. Sandy Claws will not get gifts galore if she neither comes in through chimney flue nor doggie’s door.

B. Assuming that Sandy Claws comes in through doggie’s door, unless she doesn’t get caught in pooch’s jaws she’ll exist no more.

C. Sandy Claws gets gifts galore only if she doesn’t come in through doggie’s door.

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

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

PART 5: Proof (15 points)

Instructions: Construct a proof of the following argument.

( - (P . Q) v - R)
( - (Q . R) > S)
((P > S) > S)
____________
(M > S)

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.

No cats are those who enter through doggie’s door.
Some of those who enter through doggie’s door are those who get gifts galore.
___________________

Some cats are not those who get gifts galore.

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.