PHIL 211

Introduction to Logic

EXAMINATIONS – 2018

Trimester 2

SECTION A: Propositional Logic

1.       (a) Translate the following argument into the language of propositional logic (PL):

Pablo purrs only if Lola does not bark at him.

Lola is barking at Pablo.

Therefore, Pablo is not purring.

(b) Test this argument for validity using truth tables.

(20 Marks)

2.       Do truth tables for the following two formulas. Are they equivalent? Contradictory? Or neither?

(i)       (p ⊃ q) ∨ ~q                 (ii) p ⊃ ~p

(10 Marks)

3.       Do a tree for the following argument. Is it valid? If it is invalid, give a counterexample.

p ⊃ (q ∨ ~r)

~(p ⊃ p) ⊃ r

/ : ~p

(10 Marks)

4.       Do a tree for the following argument. Is it valid? If it is invalid, give a counterexample.

p ∨ ~q

p ⊃ r

~q ⊃ r

/ : ~~~~r

(10 Marks)

SECTION B: Quantificational Logic

5.       Translate the following English sentences into the language of quantificational logic (QL).

(a) Every cat hates some dog.

(b) No cat hates every dog who loves every mouse.

(c) Some cat hates every dog.

(d) All dogs love every cat who loves itself.

(20 Marks)

6.       (a) Eliminate the quantifiers in the following formula using two individuals (a and b).

(∀x)(Px ⊃ (∃y)(xQy ∨ yRx))

(b) Construct a finite possible world in which this formula is true (and in which only a and b exist).

(10 Marks)

7.       Do a tree for the following argument. Is it valid? If it is invalid, construct a counter-model for it.

(∀x)(Px ⊃ (∃y)Qy)

(∀z)(~~~Qz & (Pa ⊃ Pa)

/ : (∀x)~Px

(20 Marks)