Phil 105 exam
Phil 105 Exam 2 Spring 2020
Name:__________________________
For this exam, keep in mind that:
{&} Conjunctions are true if and only if both conjuncts are true.
{V} Disjunctions are false if and only if both disjuncts are false.
{→} Conditionals are false if and only if the antecedent is true and the consequent is false.
{} Biconditionals are true if and only if both sides of the biconditional match in truth value.
{~} Negations are true if and only if what is negated is false.
p
q
( p → q ) ( p & q ) ( p V q ) ( p q ) ~p
T
T
T T T T F
T
F
F T F F F
F
T
F T T F T
F
F
F F T T T
Provide truth tables for the following sentence forms, then circle the term that applies.
A
B
( ( ~A B ) → A )
CONTRADICTION TAUTOLOGY CONTINGENCY
C
D
( (C ~ D) (C D) )
CONTRADICTION TAUTOLOGY CONTINGENCY
F
G
( F → (G ~ G) )
CONTRADICTION TAUTOLOGY CONTINGENCY
Provide joint truth table for the following pair of sentences and circle the phrase that applies.
A
B
( ~ A → B ) ( A ~ B )
LOGICALLY EQUIVALENT NOT LOGICALLY EQUIVALENT
Determine whether or not the following argument forms are valid using truth tables (circle one).
A
B
Premise. ( ~A B ) Conclusion. ( B A )
VALID INVALID
X
Y
Z
Premise. ( X → Y ) Premise. ( Y Z ) Conclusion. ( Z → X )
VALID INVALID
A
B
C
Premise. ( C → A ) Premise. ( B → A ) Premise. ( C B ) Conclusion. A
VALID INVALID
Using the key {M: The match lights, S: You struck the match} for the following argument, (i) provide the form of the argument, and (ii) use a truth table to determine whether or not the argument is valid.
P. If you strike the match, then the match lights.
Q. You strike the match and it doesn’t light.
M
S
VALID INVALID
Using the key {O: Obama is President, F: Michelle is First Lady} for the following argument, (i) provide the form, and (ii) use a truth table to determine whether or not the argument is valid.
P1) Michelle is not the First Lady. P2) Neither is Obama President, nor is Michelle First Lady. C) If Michelle is not the First Lady, then Obama is not the President.
F
O
VALID INVALID
Using the key {R: our car will run, G: our car has gasoline} for the following argument, (i) provide the form, and (ii) use a truth table to determine whether or not the argument is valid.
P1) If our car doesn’t have gasoline, it won’t run. P2) Our car has gasoline. C) Our car will run.
G
R
VALID INVALID
Using the following interpretation:
E. the economy improves
F. consumers increase borrowing
G. consumer spending falls
H. unemployment rises
I. there is a housing boom
T. taxes are raised
U. government spending increases
V. stock prices will fall
W. more jobs will be created
X. interest rates will rise
Translate the following English sentences into SL:
1. The economy improves, but unemployment rises.
2. The economy improves if both taxes aren’t raised and stock prices don’t fall.
3. Government spending increases, and if more jobs are created then will there be a housing boom.
4. Consumer spending does not fall if they increase borrowing, but unemployment still rises.
5. There is a housing boom only if both government spending and consumer borrowing increases.
6. Stock prices will fall if and only if consumers don’t increase borrowing.
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