Exam 2 - Propositional Logic
Introduction to Formal Logic
Name: Melinda Weaver Date:
Please identify the co
ect translation for the following propositional statements.
1. Either Safeco reduces premiums and Geico cuts costs or Farmers hires agents.
Answer:
(S*G)yF
2. If either Nationwide or Geico does not open new offices, then Metropolitan does
not hire agents.
Answer :
(Ny G)> M
Given that A and Bare true and X and Yare false, determine the truth-value of the following
propositions using the truth functions of the logical operators.
3.
Please build a truth table for each of the following symbolic statements and then classify the
statements.
4. 5.
Please build a truth table for the following two symbolic statements and compare them to
determine if they are logically equivalent, contradictory, consistent, or Inconsistent.
6.
7.
Please construct a truth table for the following arguments and determine whether they are
valid or invalid.
8.
9.
Please construct an indirect truth table for the following argument and determine whether the
argument is valid or invalid.
10.
Truth Functions
~
P
F
T
T
F
P
•
Q
T
T
T
T
F
F
F
F
T
F
F
F
P
v
Q
T
T
T
T
T
F
F
T
T
F
F
F
P
Q
T
T
T
T
F
F
F
T
T
F
T
F
P
Q
T
T
T
T
F
F
F
F
T
F
T
F
Introduction to Formal Logic
Name: Melinda Weaver Date:
Please identify the co
ect translation for the following propositional statements.
1. Either Safeco reduces premiums and Geico cuts costs or Farmers hires agents.
Answer:
(S*G)yF
2. If either Nationwide or Geico does not open new offices, then Metropolitan does
not hire agents.
Answer :
(Ny G)> M
Given that A and Bare true and X and Yare false, determine the truth-value of the following
propositions using the truth functions of the logical operators.
3.
Please build a truth table for each of the following symbolic statements and then classify the
statements.
4. 5.
Please build a truth table for the following two symbolic statements and compare them to
determine if they are logically equivalent, contradictory, consistent, or Inconsistent.
6. Answer : Inconsistent
F
T
T
T
T
T
F
F
F
F
T
T
T
F
F
F
T
T
T
F
F
T
T
F
F
F
T
F
7.
Answer Logically Equivalent
F
T
T
T
T
F
F
T
T
T
F
F
T
F
F
F
F
T
F
F
T
F
T
T
T
F
T
F
T
F
T
T
F
T
T
F
Please construct a truth table for the following arguments and determine whether they are
valid or invalid.
8.
Answer : INVALID
T C
T>C
T XXXXXXXXXXT
T T T
F T
F T T T
F XXXXXXXXXXT
F T T
T F
T T F F
T XXXXXXXXXXF
T F F
F T
F F T T
F XXXXXXXXXXF
F T F
T F
F F F F
9.
Please construct an indirect truth table for the following argument and determine whether the
argument is valid or invalid.
10.
XXXXXXXXXXF T TF F F F T T F T F T F T F T T T F T F F F
Answer INVALID
XXXXXXXXXXNo contradiction
Truth Functions
~
P
F
T
T
F
P
•
Q
T
T
T
T
F
F
F
F
T
F
F
F
P
v
Q
T
T
T
T
T
F
F
T
T
F
F
F
P
Q
T
T
T
T
F
F
F
T
T
F
T
F
P
Q
T
T
T
T
F
F
F
F
T
F
T
F