TT: truthtable PL:predicate logic SL:sentence logic S. : sentence
In sentence logic, Our atomic sentences were just sentence letters. Over there we assigned T or F to each sentence and we filled the TT
(Truth table) for any complex sentence.
In predicate
32. QUANTIFIER SCOPE, BOUND VARIABLES, AND FREE VARIABLES
In (x)(y)Lxy'The existential quantifier binds the variables in positoin 3 rd positoin and the universal q. binds the variable at position 4, where the
nth position is where the nth variable is loc
Lets look at two arguments that are indeed valid, and see how the type of logic we have studied so far addresses
them and evaluate them:
(1) Everyone loves Adam
A
(2) Eve loves Adam
B
Eve Loves Adam
B
Someone loves Adam
C
In sentence logic, we transcribed
Volume 2. Chapter 5 (review ch 5 and 7 if vol.1)
Natural Deduction for predicate Logic fundamentals
To say that an argument is valid is to say that in every possible
case in which the premises are true, the conclusion is true also. The natural
deduction t
Spring 2010
Philosophy 3200
Exam #3
1. Provide derivations using natural deductions to prove the validity of each of the
following arguments. You must properly number and annotate your derivations.
(7 points each)
(a)
~R
R v ~Q
~Q
1
2
3
4
~R
R v ~Q
~R
~Q
Fall 2008
Philosophy 3200
MakeUp Exam
1) Which of the following expressions are sentences of sentence logic and which
are not? (3 points each)
a) ~v&CBGB
b) J & cfw_~(K v L) [H (J & ~L)]
c) (x)~(y)cfw_Hxya & [(w)Pywz (Easy v Hxrd)]
2) For each of the fol
Spring 2010
Philosophy 3200
Exam #1
1) Which of the following expressions are sentences of sentence logic and which
are not? (1 point each)
a) L v J
b) ~K & P~L
c) ~(~S v F) & ~T
d) cfw_[(~J v L) v (K & B)] & O
e) ~cfw_[F v (C & ~D)] ~& [H v (I &Q)]
YES
N
Spring 2010
Philosophy 3200
Exam #4
1) Provide derivations that establish the validity of the following arguments. You may
use any of the primitive or derived rules. (4 points each)
a)
N (C v B)
(C v B) ~T
~S T
N
S
1.  N (C v B)
2.  (C v B) ~T
3.  ~S T
PHIL 3200 EXAM #1
SPRING 2012
INSTRUCTOR: M. BERK
1. Which of the following expressions are sentences of sentence logic
(legitimate logical sentences, or wellformed formulae) and which
are not? (write yes or no)
(a) D
(b) L & F
(c) F v G & N
(d) cfw_[(P
Spring 2007
Philosophy 3200
Exam #5
In questions 1 & 2, use this transcription guide:
UD: b,e,i,j,k,n,p
b: Beatrice
e: Edgar
i: Iggy
j: Janice
k: Kalamazoo
n: Newark
p: Peoria
Cx: x is a cat
Rx: x is a road
Bxy: x is bigger than y
Gxy: x goes to y
Lxy: x
Spring 2007
Philosophy 3200
Exam #1
1) Which of the following expressions are sentences of sentence logic and which
are not? (3 points each) [15 points]
a)
b)
c)
d)
e)
A ~& B
L & (E v P)
G & ~(G v S)
(H & B v I) & [R & (v G v T)]
cfw_[K & (B v ~O)] v ~[K
Spring 2007
Philosophy 3299
Exam #2
1) For each pair of sentences below prove that they are logically equivalent.
Use the rules of logical equivalence, showing which rules you use as I have done
in class and as you have been asked to do on the homework. I
Spring 2010
Philosophy 3200
Exam #5
For questions 1 & 2 use this transcription guide:
Bx: x is a bull
Mx: x likes to drink milk
Fx: x likes to smell flowers
Pxy: x plays with y
Rxy: x rides y
Ixy: x is visiting y
a: Abigail
f: Ferdinand
i: Ike
n: Spain
p:
Fall 2008
Philosophy 3200
Exam #5
In questions 1 & 2, use this transcription guide:
UD: cfw_Students in logic class
a: Anne
Ax: x does well in logic class
b: Bob
Sx: x studies hard
c: Charlies
Lxy: x likes y
Fxy: x sits to the left of y
Rxy: x sits to the
Spring 2007
Philosophy 3200
Exam #3
1. Provide derivations using natural deductions to prove the validity of each of the
following arguments. You must properly number and annotate your derivations.
(7 points each)
(a) ~P~D
~D~F
~P
~F
1
2
3
4
5
~P~D
~D~F
~
Spring 2010
Philosophy 3200
Exam #3
1. Provide derivations using natural deductions to prove the validity of each of the
following arguments. You must properly number and annotate your derivations.
(7 points each)
(a) ~R
R v ~Q
~Q
(b) A (B v C)
~C
AB
(c)
Spring 2007
Philosophy 3200
MakeUp Exam
1) For each of the following sentences, state whether its main connective is ~,
&, v, , , (x), or (x) and list each sentences components. Then do the
same for the components you have listed until you get down to at
Spring 2007
Philosophy 3200
Exam #6
1) Provide derivations that establish the validity of the following arguments. You
may use any of the primitive or derived rules. (7 points each)
a) (x)Kx v ~(x)Dx
Da
(Kb v Cb) Jbi
(x)Jbx
1.
2.
3.
4.
5.
6.
7.
8.
9.
(x)
Fall 2008
Philosophy 3200
Exam #1
1) Which of the following expressions are sentences of sentence logic and which
are not? (3 points each)
a)
b)
c)
d)
~A
Q (& BC)
J v ~(~G & L)
cfw_[J v (D & ~A)] & [S & L v B & (S v J)]
YES
NO
YES
NO
2) For each of the fo
Fall 2008
Philosophy 3200
Exam #6
1) Prove the following Quantifier Negation rules. You may use any primitive or
derived rules, except, of course, for any of the Quantifier Negation rules.
(12 points each)
a) (x)~Fx
~(x)Fx
b) (x)~Fx
~(x)Fx
2) Provide deri
Spring 2007
Philosophy 3200
Exam #5
In questions 1 & 2, use this transcription guide:
UD: b,e,i,j,k,n,p
b: Beatrice
e: Edgar
i: Iggy
j: Janice
k: Kalamazoo
n: Newark
p: Peoria
Cx: x is a cat
Rx: x is a road
Bxy: x is bigger than y
Gxy: x goes to y
Lxy: x
Fall 2008
Philosophy 3200
Exam #6
1) Prove the following Quantifier Negation rules. You may use any primitive or
derived rules, except, of course, for any of the Quantifier Negation rules.
(12 points each)
a) (x)~Fx
~(x)Fx
1.
2.
3.
4.
5.
6.
7.
(x)~Fx


Spring 2007
Philosophy 3200
MakeUp Exam
1) For each of the following sentences, state whether its main connective is ~,
&, v, , , (x), or (x) and list each sentences components. Then do the
same for the components you have listed until you get down to at
Spring 2008
Philosophy 3200
Exam #3
1. Provide derivations using natural deductions to prove the validity of each of the
following arguments. You must properly number and annotate your derivations.
(14 points each: 28 point question: 28 total)
(a)
~S
~S
1
Fall 2008
Philosophy 3200
Exam #2
1) For each pair of sentences below prove that they are logically equivalent.
Use the rules of logical equivalence, showing which rules you use as I have done
in class and as you have been asked to do on the homework. If
Spring 2007
Philosophy 3200
Exam #2
1) For each pair of sentences below prove that they are logically equivalent.
Use the rules of logical equivalence, showing which rules you use as I have done
in class and as you have been asked to do on the homework. I
Spring 2007
Philosophy 3200
Exam #6
1) Provide derivations that establish the validity of the following arguments. You
may use any of the primitive or derived rules. (7 points each)
a) (x)Kx v ~(x)Dx
Da
(Kb v Cb) Jbi
(x)Jbx
b) (y)(My & Ry)
(y)(Lyn ~Ry)
(w
Fall 2008
Philosophy 3200
Exam #4
1) Prove the derived rule Contraposition using only primitive rules. (8 points)
XY
~Y~X
CP
1 XY
P
2
3
A
4
5
6
7
~Y
A
1,3 E
2R
35 ~I
26 I
X
Y
~Y
~X
~Y ~X
2) Prove that [~(S & T) & (S v T)] (~S T) is a logical truth. (8 p
Fall 2005
Philosophy 12
Exam #4
1) Test the following arguments for validity. Show your trees, showing which
paths are closed. Say whether the argument is valid or invalid, and if invalid give
the counterexamples provided by the finished tree. (8 points e