Some Useful Equivalences
xF x xF x
xF x xF x
x(F x P ) xF x P
x(F x P ) xF x P
x(P F x) P xF x
x(P F x) P xF x
x(F x P ) xF x P
x(F x P ) xF x P
x(F x Gx) xF x xGx
x(F x Gx) xF x xGx
xy(F x Gy) yx(F x
Practice Proofs
1
Proofs that use only Stage 1 rules
1. Associativity of &
P&(Q&R)
(P&Q)&R
2. Commutativity of &
P&Q
Q&P
3. Idempotence of &
P
2
P&P
Proofs that use CP but not Elimination or
RAA
1. W
Intro Logic
&I
d
e
d&e
d
e
e&d
I
SENTENTIAL LOGIC
&O
;&O
d&e d&e
;(d & e)
d
e
d ;e
O
d
d
de ed
I
de
;d
e
de
;e
d
O
de
ed
de
de
ed
ed
O
DN
DN
;(d e)
;d e
;O
df
d
f
d
;d
df
;f
;d
&D
: d&e
d

e

RULES OF DEDUCTION
Rule P (Premise Introduction): On any line (n) of a deduction, we may put any schema,
with [n] as the premise number. There is no citation.
Rule D (Discharge): Suppose that on some
WritingSourcesHarv00Bk Page i Tuesday, April 15, 2008 12:01 PM
Writing with Sources
A Guide for Harvard Students
Second Edition
Gordon Harvey
Hackett Publishing Company, Inc.
Indianapolis/Cambridge
i
A Guide to the World of Wine
Deciphering
a Wine Label
When shopping for wine, you will find that different
varietal wines have different labels. Here are some
things to look for on any wine label:
Tab
EMR17
DeductiveLogic
Lecture 25
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: I
EMR17
DeductiveLogic
Lecture 24
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: I
EMR17
DeductiveLogic
Lecture 29
Rules for deduction
Our system of formal deduction for quantificational logic now
has five rules:
Premise Introduction (PI)
Conditional Introduction (CI)
Truthfunction
EMR17
DeductiveLogic
Lecture 27
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: I
EMR17
DeductiveLogic
Lecture 28
More rules
Our system of formal deduction for quantificational logic
currently has three rules:
I GOOFED last
Premise Introduction (PI)
time, in suggesting
that we coul
EMR17
DeductiveLogic
Lecture 26
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: W
EMR17
DeductiveLogic
Lecture 19
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: B
EMR17
DeductiveLogic
Lecture 23
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: B
EMR17
DeductiveLogic
Lecture 21
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter five islanders: Alfred, Betty, Clara, David, and
Emma.
Al
EMR17
DeductiveLogic
Lecture 20
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter some islanders: Alfred, Betty, and some large
number of o
EMR17
DeductiveLogic
Lecture 22
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: B
EMR17
DeductiveLogic
Lecture 18
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: E
EMR17
DeductiveLogic
Lecture 17
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: I
EMR17
DeductiveLogic
Lecture 14
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: C
EMR17
DeductiveLogic
Lecture 16
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: I
EMR17
DeductiveLogic
Lecture 15
Warmup puzzle
You are visiting the island of knights, knaves, and monks. The
usual rules apply.
You encounter three islanders: Alfred, Betty, and Clara.
Alfred says: W
EMR17
DeductiveLogic
Lecture 13
Warmup puzzle
You are visiting a different (but nearby) island. Like the first
island, some inhabitants are knights, and some are knaves.
But there is a third kind of
EMR17
DeductiveLogic
Lecture 9
Warmup puzzle
You are back on the Island; as before, each inhabitant is either
a knight or a knave.
You encounter four islanders: Alfred, Betty, Clara, and David.
Alfre
EMR17
DeductiveLogic
Lecture 11
Warmup puzzle
You are visiting a different (but nearby) island. Like the first
island, some inhabitants are knights, and some are knaves.
But there is a third kind of
EMR17
DeductiveLogic
Lecture 12
Warmup puzzle
You are visiting a different (but nearby) island. Like the first
island, some inhabitants are knights, and some are knaves.
But there is a third kind of
EMR17
DeductiveLogic
Lecture 7
Warmup puzzle
The story: At the end of class one Friday afternoon, the professor announces to
her students that she will give them an exam during one of next weeks clas
EMR17
DeductiveLogic
Lecture 8
Warmup puzzle
You are back on the Island; as before, each inhabitant is either
a knight or a knave.
You encounter four islanders: Alfred, Betty, Clara, and David.
Alfre
EMR17
DeductiveLogic
Lecture 10
Warmup puzzle
Consider the following statement:
Either the boxed statement on this slide is false,
or there will be cookies during todays quiz.
What can you deduce abo