PHIL 1012 Introductory Logic Problem Set 5
9 September 2014
1. Translate the following into MPL:
Everyone runs only if someone does.
2. For each occurrence of a variable in the following formula, say whether that occurrence
is free or bound. Is the formul
PHIL 1012 Introductory Logic Problem Set 5
6 September 2016
Due in your tutorial in Week 8.
1. Translate the following into MPL:
Someone is happy only if everyone is.
2. For each occurrence of a variable in the following formula, say whether that occurren
PHIL 1012: Introductory Logic Problem Set 8
7 October 2014
Translate the following into GPL:
1. Alice is taller than Bob but not vice versa.
2. If Alice is taller than everything Bobs taller than, and Bob is taller than Alice, then Alice
is taller than he
Notes
Thursday, 28 July 2016
3:05 PM
Chapter 1
Propositions and Arguments
What is Logic?
Logic concerns itself with propositions, seeking out whether they
are true or false. Thus the area of Logic can be defined as the
science of Tr
PHIL 1012 Introductory Logic Problem Set 2
19 August 2014
1. Determine using a truth table whether the following two propositions are equivalent.
AB
(A B) (A B)
2. Is the following argument valid? Justify your answer.
(P Q) (R S)
(P Q)
RS
PHIL 1012 Introductory Logic Problem Set 4
2 September 2014
1. Determine using a tree whether the following argument is valid. If the argument is invalid, read off a counterexample from your tree.
AB
BC
AC
2. Determine using a tree whether the following a
PHIL 1012: Introductory Logic Problem Set 1
12 August 2014
Translate the following from English into PL:
1. The butler did it if and only if the gardener speaks German or chews tobacco.
2. Bill is in Parisand Ben is too only if Jill and Jen arent both the
PHIL 1012: Introductory Logic Problem Set 9
14 October 2014
1. For the following proposition, describe (i) a model on which it is true, and (ii) a model on
which it is false. If there is no model of one of these types, explain why.
xy(Px Qy) (Rxy Ryx)
2.
PHIL 1012: Introductory Logic Problem Set 6
16 September 2014
1. Here is a model:
Domain: cfw_Alex, Ben, Carol, Diana
Referents: a: Diana b: Alex
Extensions: O: cfw_Alex, Ben Y : cfw_Carol, Diana
Is the proposition Oa x(Ox Y x) true or false in this model
PHIL 1012: Introductory Logic Problem Set 7
23 September 2014
1. Determine using a tree whether the following argument is valid. If the argument is invalid, read off a countermodel from your tree.
x(Fx Gx)
xGx
xFx
2. Determine using a tree whether the fo
PHIL 1012: Introductory Logic Problem Set 10
21 October 2014
1. Translate the following into GPLI:
Maggie is neither the youngest nor the oldest in her class.
2. For the following proposition, describe (i) a model on which it is true and (ii) a model on
w
PHIL 1012 Introductory Logic Problem Set 7
20 September 2016
Due in your tutorial in Week 10.
1. Determine using a tree whether the following argument is valid. If the argument is invalid, read off a countermodel from your tree.
x(Fx Gx)
xFx
xGx
2. Deter
PHIL 1012 Introductory Logic Problem Set 9
11 October 2016
Due in your tutorial in Week 12.
Translate the following into GPL:
1. Anything taller than something Alice is taller than is taller than Alice.
2. If Alice is taller than everything Bobs taller th
PHIL 1012 Introductory Logic Problem Set 8
4 October 2016
Due in your tutorial in Week 11.
Translate the following into GPL:
1. Alice is taller than Bob but not vice versa.
2. Someone can hear Alice but Alice cant hear anything.
PHIL 1012 Introductory Logic Problem Set 3
23 August 2016
Due in your tutorial in Week 6.
1. Translate the following into PL:
Knuckles will bark unless he gets fed or walked (or both).
2. Give a proposition involving only the connectives and that is equiv
PHIL 1012 Introductory Logic Problem Set 6
13 September 2016
Due in your tutorial in Week 9.
1. Here is a model:
Domain: cfw_Adrian, Boris, Claire, Dana
Referents: a: Dana b: Adrian
Extensions: O: cfw_Adrian, Boris Y : cfw_Claire, Dana
Is the proposition
PHIL 1012 Introductory Logic Problem Set 2
16 August 2016
Due in your tutorial in Week 5.
1. Write out a truth table for the following proposition, and state whether it is a tautology, a
contradiction, or neither:
(A (B C) (A B) (A C)
2. Is the following
PHIL 1012 Introductory Logic Problem Set 10
18 October 2016
Due in your tutorial in Week 13.
1. For the following proposition, describe (i) a model on which it is true, and (ii) a model on
which it is false. If there is no model of one of these types, exp
PHIL 1012 Introductory Logic Problem Set 10
Answers
1. These are just examplesthere are infinitely many other correct answers:
(i) one way: any model where the extension of P or Q (or both) empty.
another way:
domain: cfw_1, 2
extensions:
P : cfw_1
Q : cf
PHIL 1012 Introductory Logic Problem Set 1
9 August 2016
Due in your tutorial in Week 4.
1. Translate the following from English into PL:
If roses are red or violets are blue, then honey is sweet and bananas arent green.
2. Write out a construction for th
PHIL 1012 Introductory Logic Problem Set 4
30 August 2016
Due in your tutorial in Week 7.
1. Determine using a tree whether the following argument is valid. If the argument is invalid, read off a counterexample from your tree.
AB
CB
C A
2. Determine using
PHIL 1012 Introductory Logic Problem Set 3
26 August 2014
1. Give the truth table for the following proposition:
(A3 B) Y (A14 B)
2. Is cfw_, a functionally complete set of connectives? Justify your answer.
PHIL 1012 Introductory Logic Problem Set 2
1. Determine using a truth table whether the following two propositions are equivalent.
AB
(A B) (A B)
2. Is the following argument valid? Justify your answer.
(C D)
(A B) (C D)
AB
PHIL 1012 Introductory Logic Problem Set 1
Due in your tutorial in Week 4
Translate the following from English into PL:
1. The butler did it if and only if it is not the case that either the gardener speaks German or he
doesnt chew tobacco.
2. Bill is in
All recursive definitions have a base clause
Why syntax has to be recursive? The syntax has to be finite set of rules and capable of defining
infinitely many sentences of the language. The set of wff for PL is inifite, as with English language.
Basic prop
PHIL 1012 Introductory Logic Problem Set 2
07 July 2017
Due in tutorial Monday July 10
1. Determine using a truth table whether the following two propositions are equivalent.
AB
(A B) (A B)
2. Is the following argument valid? Justify your answer.
(P Q) (R
PHIL 1012 Introductory Logic Problem Set 5
12 July 2017
1. Translate the following into MPL:
Everyone runs only if someone does.
2. For each occurrence of a variable in the following formula, say whether that occurrence
is free or bound. Is the formula op
PHIL 1012 Introductory Logic Problem Set 3
10 July 2017
1. Give the truth table for the following proposition:
(A3 B) Y (A14 B)
2. Is cfw_, a functionally complete set of connectives? Justify your answer.
PHIL 1012 Introductory Logic Problem Set 4
11 July 2017
1. Determine using a tree whether the following argument is valid. If the argument is invalid, read off a counterexample from your tree.
AB
BC
AC
2. Determine using a tree whether the following argum
PHIL 1012 Introductory Logic Problem Set 1
05 July 2017
Translate the following from English into PL:
1. The butler did it if and only if the gardener speaks German and doesnt chews tobacco.
2. Bill is in Paris and Ben is too, only if Jill or Jen are ther