LGIC 010 & PHIL 005
Problem Set 9
Spring Term, 2012
For each of the following pairs consisting of a set of schemata X and a schema S determine
whether X implies S. If so, provide a deduction to establish the implication. If not, specify
a structure which
LGIC 010 & PHIL 005
Problem Set 6
Spring Term, 2010
We say that a schema S admits a positive natural number n if and only if there is a
structure A of size n which satises S . (Recall that the size of a structure is the number of
members of its universe o
LGIC 010 & PHIL 005
Problem Set 5
Spring Term, 2010
1. Let S1 be the following schema.
(x)Lxx (x)(y )(Lxy Lyx) (x)(y )(z )(Lyz (w)(Lxw (w = y w = z )
(a) (10 points) Specify a structure A1 of size at least 4 which satises S1 , that is, U A1
has at least 4
LGIC 010 & PHIL 005
Problem Set 4
Spring Term, 2010
1. (25 points) How long a list of pure monadic schemata involving only the predicate
letters F, G, and H can be constructed so that no two schemata on the list are
equivalent?
2. (25 points) How long a l
LGIC 010 & PHIL 005
Problem Set 10
Spring Term, 2009
For each of the following pairs consisting of a set of schemata X and a schema S determine
whether X implies S. If so, provide a deduction to establish the implication. If not, specify
a structure which
LGIC 010 & PHIL 005
Problem Set 9
Spring Term, 2009
For each of the problems 1 3 below, determine whether or not the premises imply the
conclusion. If so, present a deduction of the conclusion from the premises; if not, specify a
structure in which the pr
LGIC 010 & PHIL 005
Problem Set 8
Spring Term, 2009
1. Let A be the structure interpreting a single dyadic predicate letter R with U A =
cfw_1, 2, 3 and RA = cfw_ 1, 2 , 2, 1 .
(a) (10 points) List all the automorphisms of A.
(b) (10 points) List all sets
LGIC 010 & PHIL 005
Problem Set 7
Spring Term, 2009
Taking the universe of discourse to be the set of positive integers cfw_1, 2, . . . and using the
dyadic predicate letter P to express the relation 2 is divisible 1 and the triadic predicate
letter R to
LGIC 010 & PHIL 005
Problem Set 6
Spring Term, 2009
We say that a schema S admits a positive natural number n if and only if there is a
structure A of size n which satises S .
1. (25 points) Write down a schema S involving only the dyadic predicate letter
LGIC 010 & PHIL 005
Problem Set 5
Spring Term, 2009
1. Let S1 be the following schema.
(x)Lxx (x)(y )(Lxy Lyx) (x)(y )(z )(Lxz y = z )
(a) (10 points) Specify a structure A1 of size at least 4 which satises S1 , that is, U A1
has at least 4 members and A1
LGIC 010 & PHIL 005
Problem Set 4
Spring Term, 2009
1. (25 points) How long a list of pure monadic schemata involving only the predicate
letters F and G can be constructed so that no two schemata on the list are
equivalent?
2. (25 points) How long a list
LGIC 010 & PHIL 005
Problem Set 3
Spring Term, 2009
1. (25 points) How many structures with universe of discourse cfw_1, 2, 3, 4, 5 interpreting
only the monadic predicate letters F and G make true the schema
(x)(F x Gx).
2. (25 points) Write down a satis
LGIC 010 & PHIL 005
Problem Set 2
Spring Term, 2009
1. (20 points) Let S be the following truth-functional schema:
(p1 q1 ) (p2 q2 ) (p3 q3 ) (p4 q4 ) (p5 q5 ).
How many truth assignments to the ten sentence letters p1 , . . . , p5 , q1 , . . . , q5 satis
LGIC 010 & PHIL 005
Problem Set 1
Spring Term, 2009
1. (24 points) Test the following schemata for validity.
(a) (p q ) (q p)
(b) (p q ) (p q ) (Recall that represents exclusive disjunction.)
2. (65 points) In each case, determine whether the rst schema i
LGIC 010 & PHIL 005
Problem Set 7
Spring Term, 2010
Taking the universe of discourse to be the set of positive integers cfw_1, 2, . . . and using
the triadic predicate letter P to express the relation 3 is the product of 1 and 2
and the dyadic predicate l
LGIC 010 & PHIL 005
Problem Set 8
Spring Term, 2010
1. Let A be the structure interpreting a single dyadic predicate letter R with U A =
cfw_1, 2, 3 and RA = cfw_ 1, 2 .
(a) (10 points) List all the automorphisms of A.
(b) (10 points) List all sets which
LGIC 010 & PHIL 005
Problem Set 8
Spring Term, 2012
1. Let A be the structure interpreting a single dyadic predicate letter R with U A =
cfw_1, 2, 3 and RA = cfw_ 1, 2 , 2, 2 , 3, 2 .
(a) (10 points) List all the automorphisms of A.
(b) (10 points) List a
LGIC 010 & PHIL 005
Problem Set 7
Spring Term, 2012
Taking the universe of discourse to be the set of positive integers cfw_1, 2, . . . and using
the triadic predicate letter P to express the relation 3 is the product of 1 and 2
and the dyadic predicate l
LGIC 010 & PHIL 005
Problem Set 6
Spring Term, 2012
We say that a schema S admits a positive natural number n if and only if there is a
structure A of size n which satises S .
1. (25 points) Write down a schema S involving only the monadic predicate lette
LGIC 010 & PHIL 005
Problem Set 5
Spring Term, 2012
1. Let S1 be the following schema.
(x)(y )Lxy
(a) (10 points) Specify a structure A1 of size at least 3 which satises S1 , that is, U A1
has at least 3 members and A1 |= S1 .
U A1 =
LA1 =
(b) (10 points)
LGIC 010 & PHIL 005
Problem Set 4
Spring Term, 2012
1. (25 points) How long a list of pure monadic schemata involving only the predicate
letters F and G can be constructed so that no two schemata on the list are
equivalent?
2. (25 points) How long a list
LGIC 010 & PHIL 005
Problem Set 3
Spring Term, 2012
1. (25 points) How many structures with universe of discourse cfw_1, 2 interpreting only
the monadic predicate letters F and G make true the schema
(x)(F x Gx).
2. (25 points) Write down a satisable sche
LGIC 010 & PHIL 005
Problem Set 2
Spring Term, 2012
1. (25 points) Is there a list of 7 schemata involving only the sentence letters p and q
such that no schema on the list implies any other schema on the list?
2. (25 points) How long a list of truth-fun
LGIC 010 & PHIL 005
Problem Set 1
Spring Term, 2012
1. (33 points) Test the following schemata for validity.
(a) (p q ) (p r) (q r)
(b) (p q ) (q p)
(c) (p (q r) (p q ) r) (Recall that represents exclusive disjunction.)
2. (55 points) In each case, determ
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LGIC 010 & PHIL 005
Practice Examination II
Spring Term, 2013
1. (10 points) How long a list of pure monadic schemata involving only the predicate
letters F and G can be constructed so that no two schemata on the list are
equivalent, and no sc
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LGIC 010 & PHIL 005
Practice Examination II
Spring Term, 2013
1. (10 points) How long a list of pure monadic schemata involving only the predicate
letters F and G can be constructed so that no two schemata on the list are equivalent, and no sc
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LGIC 010 & PHIL 005
Practice Examination I
Spring Term, 2013
1. (20 points) For each of the following truth-functional schemata, indicate in the space
provided whether it is valid, satisbale but not valid, or unsatisable.
(a) (p q ) (p q )
uns
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LGIC 010 & PHIL 005
Practice Examination I
Spring Term, 2013
1. (20 points) For each of the following truth-functional schemata, indicate in the space
provided whether it is valid, satisbale but not valid, or unsatisable.
(a) (p q ) (p q )
(b)
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LGIC 010 & PHIL 005 Practice Final Examination
Spring Term, 2013
1. (30 points) Taking the universe of discourse to be the set of positive integers cfw_1, 2, . . .
and using the triadic predicate letter P to express the relation 3 is the produ