Question 1

construct theories for which the following interpretation is a model (i.e. construct at least two sentences which are true under the given interpretation). Domain = {1, 2, 3, ..., 28, 29, 30} a = 1 e = 21 b = 2 f = 23 c = 4 g = 27 d = 19 h = 29 Ex = {2, 4, 6, ..., 28, 30} Ox = {1, 3, 5, ..., 27, 29} Px = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29} Sxyz = The set of all triples such that the first is the sum of the second and third {<2, 1, 1>, <3, 1, 2>, <3, 2, 1>, <4, 1, 3>, <4, 2, 2>, <4, 3, 1>, <5, 1, 4>, ... } -Construct a theory of at least two sentences which uses at least two constants.

Accepted Answer

The answer of construct theories for which the following interpretation...

Question 2

construct theories for which the following interpretation is a model (i.e. construct at least two sentences which are true under the given interpretation). Domain = {1, 2, 3, ..., 28, 29, 30} a = 1 e = 21 b = 2 f = 23 c = 4 g = 27 d = 19 h = 29 Ex = {2, 4, 6, ..., 28, 30} Ox = {1, 3, 5, ..., 27, 29} Px = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29} Sxyz = The set of all triples such that the first is the sum of the second and third {<2, 1, 1>, <3, 1, 2>, <3, 2, 1>, <4, 1, 3>, <4, 2, 2>, <4, 3, 1>, <5, 1, 4>, ... } -Construct a theory of at least two sentences, at least one of which uses an existential quantifier.

Accepted Answer

The answer of construct theories for which the following interpretation...

Question 3

construct theories for which the following interpretation is a model (i.e. construct at least two sentences which are true under the given interpretation). Domain = {1, 2, 3, ..., 28, 29, 30} a = 1 e = 21 b = 2 f = 23 c = 4 g = 27 d = 19 h = 29 Ex = {2, 4, 6, ..., 28, 30} Ox = {1, 3, 5, ..., 27, 29} Px = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29} Sxyz = The set of all triples such that the first is the sum of the second and third {<2, 1, 1>, <3, 1, 2>, <3, 2, 1>, <4, 1, 3>, <4, 2, 2>, <4, 3, 1>, <5, 1, 4>, ... } -Construct a theory of at least two sentences, at least one of which uses a universal quantifier.

Accepted Answer

The answer of construct theories for which the following interpretation...

Question 4

construct theories for which the following interpretation is a model (i.e. construct at least two sentences which are true under the given interpretation). Domain = {1, 2, 3, ..., 28, 29, 30} a = 1 e = 21 b = 2 f = 23 c = 4 g = 27 d = 19 h = 29 Ex = {2, 4, 6, ..., 28, 30} Ox = {1, 3, 5, ..., 27, 29} Px = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29} Sxyz = The set of all triples such that the first is the sum of the second and third {<2, 1, 1>, <3, 1, 2>, <3, 2, 1>, <4, 1, 3>, <4, 2, 2>, <4, 3, 1>, <5, 1, 4>, ... } -Construct a theory of at least three sentences, at least one of which uses an existential quantifier and at least one of which uses a universal quantifier.

Accepted Answer

The answer of construct theories for which the following interpretation...

Question 5

construct theories for which the following interpretation is a model (i.e. construct at least two sentences which are true under the given interpretation). Domain = {1, 2, 3, ..., 28, 29, 30} a = 1 e = 21 b = 2 f = 23 c = 4 g = 27 d = 19 h = 29 Ex = {2, 4, 6, ..., 28, 30} Ox = {1, 3, 5, ..., 27, 29} Px = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29} Sxyz = The set of all triples such that the first is the sum of the second and third {<2, 1, 1>, <3, 1, 2>, <3, 2, 1>, <4, 1, 3>, <4, 2, 2>, <4, 3, 1>, <5, 1, 4>, ... } -Construct a theory of at least three sentences which uses all three predicates and at least three different constants.

Accepted Answer

The answer of construct theories for which the following interpretation...

Question 6

provide a conterexample in a finite domain to each given invalid argument.
-1. Ad ⊃ (∀x)Fdx / (∃x)Fdx

Accepted Answer

The answer of provide a conterexample in a finite domain...

Question 7

provide a conterexample in a finite domain to each given invalid argument.
-1. (∃x)(Dxa • Ex)
2. (∃x)(Dxa • Fx) / (∃x)(Ex • Fx)

Accepted Answer

The answer of provide a conterexample in a finite domain...

Question 8

provide a conterexample in a finite domain to each given invalid argument.
-1. (∀x)[Hx ⊃ (∃y)(Iy • Jxy)]
2. Ha
3. Ib / Jab

Accepted Answer

The answer of provide a conterexample in a finite domain...

Question 9

provide a conterexample in a finite domain to each given invalid argument.
-1. (?x)[Px ? (?y)Qxy]
2. (?x)[(?y)Qxy ? (?y)Rxy]
3. Pa / Rab

Accepted Answer

The answer of provide a conterexample in a finite domain...

Question 10

provide a conterexample in a finite domain to each given invalid argument.
-1. (∀x)[(∃y)(Fxy • Gy) ⊃ (∀y)(Gy ⊃ Fxy)]
2. Ga / (∀x)(Fxa ⊃ Fax)

Accepted Answer

The answer of provide a conterexample in a finite domain...

Question 11

derive the conclusions of each of the following arguments using the rules of inference for F.
-1. (?x)[Ex ? (?y)(Fy • Gxy)]
2. (?x)(Ex • Hxb) / (?x)(?y)(Gxy • Hxy)

Accepted Answer