PHIL 211
INTRODUCTION TO LOGIC
EXAMINATIONS - 2017
TRIMESTER 1
SECTION A: Propositional Logic
1. Translate the following statements into Propositional Logic (PL). Use the dictionary provided.
Dictionary:
B = Ignorance is bliss.
M= Cereal tastes better with milk.
Y= Your cat is ignoring you.
S= The earth revolves around the sun.
a. Cereal does not taste better with milk unless the earth does not revolve around the sun.
b. Cereal tastes better with milk if and only if ignorance is bliss.
c. Only if your cat is ignoring you, does cereal taste better with milk.
d. Either the earth revolves around the sun or ignorance is bliss, and not both.
e. Although your cat is ignoring you, it is not both the case that the earth revolves around the sun and cereal tastes better with milk.
(10 Marks)
2. Draw truth tables for the following:
a. Draw a truth table for the following pair of formulas. How are they related? (Are they equivalent, contradictory, contrary, sub-contrary, does the first tautologically imply the second, does the second tautologically imply the first, or none of the preceding?)
b. Draw a truth table to determine whether or not the following argument is valid. State whether or not it is valid.
(10 Marks)
3. Draw truth trees for the following:
a. Draw a truth tree to determine whether or not the following argument is valid. State whether or not it is valid. If it is invalid, please present a counterexample.
b. Draw a truth tree to determine whether or not the following formula is a tautology. State whether or not it is a tautology.
(10 Marks)
4. Prove that the following arguments are valid by deriving them in SD+. (The rules sheet for SD and SD+ is attached, in case you need to refer to it.)
(20 Marks)
SECTION B: Predicate Logic
5. Translate the following statements into the language of monadic quantification theory (MQT). Use the predicates provided.
Universe of discourse = all animals
Vocabulary:
Cx = x is a cat
Px = x is a pukeko
Bx = x is a bird
Hx= x is healthy
Gx= x is green
Statements:
a. All pukekos are birds.
b. No cats are pukekos.
c. Only birds are pukekos.
d. If any pukeko is green then not all pukekos are healthy.
e. Some healthy cats are not green.
(5 Marks)
6. Expand the following formulas and test them in the finite possible world given below.
(10 Marks)
7. Translate the following sentences into the language of QT (with identity if necessary) using the vocabulary given.
Domain of discourse = all animals
Vocabulary:
Gx = x is green
Cx = x is a cat
Bx = x is a bird
Px = x is a pukeko
xBy = x is bigger than y
b=Boris
g=Gregory
a. No pukeko is bigger than Boris.
b. There is a green bird that is bigger than every cat.
c. All pukekos except Boris and Gregory are non-green.
d. There is at most one green cat.
e. Some bird is bigger than exactly one cat.
(10 Marks)
8. Produce a truth tree to determine whether or not the following formula is a tautology. If it is not a tautology, then produce a possible world in which it is false.
(5 Marks)
9. Using the truth-tree method, determine whether the following set of formulas is consistent. If it is consistent, produce a possible world showing it to be consistent.
(5 Marks)
10. Produce a truth tree to determine whether or not the following argument is valid. If it is not valid, then produce a possible world as a counterexample.
(5 Marks)
11. Produce a truth tree to determine whether or not the following formulas are
tautologies. If a formula is not a tautology, then produce a possible world in which it is false.
(10 Marks)