PHIL 211

INTRODUCTION TO LOGIC

EXAMINATIONS – 2019

Trimester 1

SECTION A: PROPOSITIONAL LOGIC

1. Translate the following statements into Propositional Logic (PL). Use the dictionary provided.

Dictionary:

N = Napoleon surrendered at Waterloo.

M = Mammoths lived in the last ice age.

D = Dinosaurs lived in the last ice age.

Statements:

a. Mammoths lived in the last ice age, but dinosaurs did not.

b. Mammoths lived in the last ice age, only if Napoleon surrendered at Waterloo.

c. Unless mammoths lived in the last ice age, Napoleon did not surrender at Waterloo.

d. Mammoths and dinosaurs did not both live in the last ice age.

e. Neither mammoths nor dinosaurs lived in the last ice age, if Napoleon did not surrender at Waterloo. (10 Marks)

2.

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.

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 is attached, in case you need to refer to it.)

(20 Marks)

SECTION B: PREDICATE LOGIC

5. Symbolize the following in the language of QT, using the following dictionary:

Px: x is a pukeko

Dx: x is a duckling

Hx: x is hungry

xEy: x eats y

b: Bert

(a) All pukekos are hungry.

(b) Not all ducklings are hungry.

(c) No pukekos are hungry.

(d) Bert is a hungry pukeko.

(e) If any duckling is a pukeko then Bert eats himself.

(f) No ducklings eats any pukeko.

(g) Only hungry pukekos eat ducklings.

(h) Many pukekos are not hungry.

(i) Some ducklings eat themselves.

(j) Nothing is both a pukeko and a duckling. (20 Marks)

6. Expand the following formulas and test them in the finite possible world given below:

(10 Marks)

7. Produce a truth-tree to determine whether the following formulas are tautologies. If is not a tautology, state a counterexample.

(10 Marks)

8. Draw a truth-tree to determine whether the following argument is valid. If the argument is invalid, state a counterexample.

(10 Marks)