1. 2 exam #3 25 translations from english into predicate logic 4 points each only final formula is...
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EXAM #3EXAM #3
25 translations from English
into Predicate Logic
4 points each
Only final formula is graded.
Do intermediate work on scratch paper.
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EXAM TOPICS 1EXAM TOPICS 1
if anyone is F, then everyone is H16i‘any’
if everyone is F, then everyone is H36hmultiple quantification
every A and B is C16gdisjunctive combinations
every F S is HAPPY16econjunctive combinations
only SENIORS are HAPPY16f‘only’
every SENIOR is HAPPY26cspecified quantifiers
everyone is HAPPY 26bsimple quantifiers
JAY and KAY are HAPPY26aun-quantified formulas
example#HWChapter 6
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EXAM TOPICS 2EXAM TOPICS 2
every F RESPECTS some G27d2 quantifiers, 3 predicates
no STUDENT RESPECTS everyone27c2 quantifiers, 2 predicates
everyone RESPECTS someone27b2 quantifiers, 1 predicate
KAY RESPECTS every STUDENT21 quantifier, 2 predicates
everyone RESPECTS KAY27a1 quantifier, 1 predicate
Example#HWChapter 7
every one who RESPECTS every F RESPECTS every G
27ecomplex predicates
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Review – 1 Quantifier, 1 PredicateReview – 1 Quantifier, 1 Predicate
x Rxjno-one respects Jay
x Rxkevery one respects Kay
x RjxJay respects some one
ReviewReview – 1 Quantifier, 2 Predicates – 1 Quantifier, 2 Predicates
x ( Fx & Rxj )no F respects Jay
x ( Fx Rxk )every F respects Kay
x ( Fx & Rjx )Jay respects some F
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Review – 2 Review – 2 QuantifiersQuantifiers, 1 Predicate, 1 Predicate
x y Ryxthere is someone whom no-one respects
x y Rxythere is someone who respects no-one
x y Ryxthere is someone whom everyone R’s
x y Rxyeveryone respects someone (or other)
x y Ryxno-one is respected by everyone
x y Rxyno-one respects everyone
x y Rxysomeone respects someone
x y Rxyeveryone respects everyone
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Review – 2 Quantifiers, 2 PredicatesReview – 2 Quantifiers, 2 Predicates
x y ( Gy & Rxy )there is someone who R’s no G
x ( Fx & yRxy )there is some F who R’s everyone
x y ( Gy Rxy )no one respects every G
x ( Fx yRxy )every F respects someone (or other)
x y ( Gy & Rxy )some one respects some G
x ( Fx yRxy )every F respects everyone
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Review – 2 Quantifiers, 3 PredicatesReview – 2 Quantifiers, 3 Predicates
x ( Fx & y(Gy & Rxy) )there is some F who R’s no G
x ( Fx & y(Gy Rxy) )there is some F who R’s every G
x ( Fx & y(Gy Rxy) )no F respects every G
x ( Fx y(Gy & Rxy) )every F respects some G (or other)
x ( Fx & y(Gy & Rxy) )some F respects some G
x ( Fx y(Gy Rxy) )every F respects every G
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Complex PredicatesComplex Predicates
Simple Predicates
Pxx is a Politician
no further analysis required
Cxx is a Citizen
Complex Predicates
no Citizen Respects x
Jay Respects x
x Respects everyone must be further analyzed
x
x Respects him/herself
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Example AnalysesExample Analyses
y ( Cy & Ryx )no Citizen Respects x
y ( Cy Ryx )every Citizen Respects x
y ( Py Rxy )x Respects every Pol
y ( Py & Rxy )x Respects at least one Pol
y Ryxsomeone Respects x
y Rxyx Respects everyone
Rxxx Respects him/herself
RjxJay Respects x
Rxkx Respects Kay
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Example 1Example 1
y ( Py & Rxy )
x R’s at least one P
xCxx
every citizen respects at least one politician
x { Cx y ( Py & Rxy ) }
respects at least one politicianevery citizen
isevery C
{ }
then you if you are C you are
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x
Example 2Example 2
no politician is respected by every citizen
y ( Cy Ryx )
every C Respects x
x is R’ed by every C
}&Pxx
x { Px & y ( Cy Ryx ) }
respected by every citizenno politician
no P is
is
there is no one who is P and who is
{
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Example 3Example 3
every one who respects every pol is a moron
y ( Py Rxy )
x R’s every Politician
Mxx{x
Misevery
x { y(Py Rxy) Mx }
a moronisone who respects every Pevery
}
you are Mthenif you are you
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Example 4Example 4
x { y(Py Rxy) y(Py Ryx) }
respected by every P
every one who respects every Pol is respected by every Pol
y ( Py Ryx )y ( Py Rxy )
x is R’ed by every Px R’s every P
xx{x
is every
}
one who R’s every Pevery is
you are then if you are you
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x
Example 5Example 5
x { y ( Py Rxy ) & Rxx }
who is and who is there is no one
no one who respects every pol respects him/herself
Rxxy (Py Rxy )
x R’s him/herselfx R’s every P
}&x{x
x is x is there is no x :
isno
respects him/herselfone who R’s every Pno