Section 4.07 Self Quiz

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Consider the following domain, assignment of objects in the domain, and assignments sets to predicates.

Domain = {Integers}

Ex: x is even

Ox: x is odd

Px: x is a positive number

Qx: x is a prime number

a: 0

b: 5

c: -4

d: 2

Given the customary truth tables, which of the following theories is modeled by the above interpretation?

Pb • ~(Pa ∨ Pd)

Pc • ~(Pa ∨ Pb)

Pb • (Pd ⊃ Pc)

Pb • ~(Pa ∨ Pc)

Pd • (Pb ⊃ Pc)

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Consider the following domain, assignment of objects in the domain, and assignments sets to predicates.

Domain = {Integers}

Ex: x is even

Ox: x is odd

Px: x is a positive number

Qx: x is a prime number

a: 0

b: 5

c: -4

d: 2

Given the customary truth tables, which of the following theories is modeled by the above interpretation?

Pb • ~Pc
Qb • ~Qc
(∃x)(Px • ~Qx)

Pc • ~Pa
Qb • ~Qc
(∃x)(Px • ~Qx)

Pb • ~Pc
Qb • ~Qc
~(∃x)(Px • Qx)

Pb • ~Pc
Qb • ~Qc
(∀x)(Px ⊃ ~Qx)

Pb • ~Pc
Qa • ~Qc
(∀x)(Px ⊃ Qx)

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Consider the following domain, assignment of objects in the domain, and assignments sets to predicates.

Domain = {Integers}

Ex: x is even

Ox: x is odd

Px: x is a positive number

Qx: x is a prime number

a: 0

b: 5

c: -4

d: 2

Given the customary truth tables, which of the following theories is modeled by the above interpretation?

(∃x)(Ex • Px)
(∀x)(Ex ⊃ Px)

(∀x)(Ex ⊃ Qx)
~(∀x)(Ex ⊃ Px)

(∃x)(Ex • Px)
~(∀x)(Ex ⊃ Px)

(∃x)(Ex • Px)
∀x)(Ex ⊃ ~Px)

(∃x)(Ex • Ox)
~(∀x)(Ex ⊃ Px)

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Consider the following domain, assignment of objects in the domain, and assignments sets to predicates.

Domain = {Integers}

Ex: x is even

Ox: x is odd

Px: x is a positive number

Qx: x is a prime number

a: 0

b: 5

c: -4

d: 2

Given the customary truth tables, which of the following theories is modeled by the above interpretation?

(∃x)(Ex • Px)
~(∃x)(Ex • Px)
(Ea • Ec) • (Ed • ~Eb)

(∀x)(Qx ⊃ Ox)
(∃x)(Ex • ~Qx)
(Ea • Ec) • (Ed • ~Eb)

(∀x)(Ex ⊃ ~Qx)(∃x)(Ex • ~Px)
(Ea • Ec) • (Pd • ~Pb)

(∃x)(Ex • Ox)
(∃x)(Ex • ~Ox)
(Ea • Ec) • (Pd • ~Pb)

(∃x)(Ex • Px)
(∃x)(Ex • ~Px)
(Ea • Ec) • (Ed • ~Eb)

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Consider the following domain, assignment of objects in the domain, and assignments sets to predicates.

Domain = {Integers}

Ex: x is even

Ox: x is odd

Px: x is a positive number

Qx: x is a prime number

a: 0

b: 5

c: -4

d: 2

Given the customary truth tables, which of the following theories is modeled by the above interpretation?

(∀x)(Ex ⊃ ~Ox)
Ec • Pd
(∀x)(Ox ⊃ ~Qx)

(∀x)(Ex ⊃ ~Px)
Ec • Pc
~(∀x)(Ox ⊃ Qx)

(∀x)(Ex ⊃ ~Qx)
Qc • Qb
~(∀x)(Ox ⊃ Qx)

(∀x)(Ex ⊃ ~Ox)
Ec • Pd
~(∀x)(Ox ⊃ Qx)

~(∀x)(Ex ⊃ Ox)
Oa • Ob
~(∀x)(Ox ⊃ Qx)

. Consider the following domain, assignment of objects in the domain, and assignments sets to predicates.

Domain = {A, B, C, ... X, Y, Z}

Cx = {B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z}
Hx = {A, H, P, Y}
Vx = {A, E, I, O, U, Y}

a = A
b = B
c = C
Given the customary truth tables, which of the following theories is modeled by the above interpretation?

Cb • Vc) • ~Ca
Va • (~Cb • ~Hc)

(Cb • Cc) • ~Ca
Va • (~Vb • ~Vc)

(Cb • Vc) • ~Ca
(∀x)Cx • (Cb • ~Hc)

(Cb • Vc) • ~Ca
(∀x)Hx • (Cb • ~Vc)

(∃x)Cx • (∃x)~Cx
(Cb • Hc) • ~Vc

. Consider the following domain, assignment of objects in the domain, and assignments sets to predicates.

Domain = {A, B, C, ... X, Y, Z}

Cx = {B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z}
Hx = {A, H, P, Y}
Vx = {A, E, I, O, U, Y}

a = A
b = Bv
c = C
Given the customary truth tables, which of the following theories is modeled by the above interpretation?

(∃x)Cx • (∃x)~Cx
(∀x)Vx • (∃x)Vx

(∃x)Cx • (∀x)~Cx
(∃x)Vx • (∃x)~Vx

(∀x)Cx • (∃x)~Cx
(∃x)Vx • (∃x)~Vx

(∃x)Cx • (∃x)~Cx
(∃x)Vx • (∃x)~Vx

(∃x)Cx • (∃x)~Cx
(∃x)Vx • (∀x)~Vx

. Consider the following domain, assignment of objects in the domain, and assignments sets to predicates.

Domain = {A, B, C, ... X, Y, Z}

Cx = {B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z}
Hx = {A, H, P, Y}
Vx = {A, E, I, O, U, Y}

a = A
b = B
c = C
Given the customary truth tables, which of the following theories is modeled by the above interpretation?

Hb • ~(Hb • Hc)
(∃x)Hx • ~(∀x)Hx

Ha • ~(Hb • Hc)
(∃x)Hx • ~(∀x)Hx

Vb • ~(Hb ∨ Ha)
(∃x)Hx • ~(∀x)H

Va • ~(Hb ∨ Hc)
(∃x)~Hx • (∀x)~Hx

Cb • ~(Hb • Hc)
(∃x)Hx • (∀x)Hx

. Consider the following domain, assignment of objects in the domain, and assignments sets to predicates.

Domain = {A, B, C, ... X, Y, Z}

Cx = {B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z}
Hx = {A, H, P, Y}
Vx = {A, E, I, O, U, Y}

a = A
b = B
c = C
Given the customary truth tables, which of the following theories is modeled by the above interpretation?

(∃x)(Cx • ~Vx)
(∃x)(Vx • ~Cx)
(∃x)(Cx • Vx)

(∃x)(Cx • ~Vx)
(∀x)(Vx ⊃ ~Cx)
(∃x)(Cx • Vx)

(∃x)(Cx • ~Vx)
(∃x)(~Vx • ~Cx)
(∃x)(Cx • Vx)

(∀x)(Cx ⊃ ~Vx)
(∀x)(Vx ⊃ ~Cx)
(∃x)(Cx • Vx)

(∃x)(Cx • Hx)
(∃x)(Vx • ~Cx)
(∃x)~(Vx ∨ Cx)

. Consider the following domain, assignment of objects in the domain, and assignments sets to predicates.

Domain = {A, B, C, ... X, Y, Z}

Cx = {B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z}
Hx = {A, H, P, Y}
Vx = {A, E, I, O, U, Y}

a = A
b = B
c = C
Given the customary truth tables, which of the following theories is modeled by the above interpretation?

(∃x)(Hx • Cx) • (∀x)(Hx ⊃ ~Cx)
(∃x)(Hx • Vx) • ~(∀x)(Hx ⊃ Vx)

(∃x)(Hx • Cx) • ~(∀x)(Hx ⊃ Cx)
(∃x)(Hx • Vx) • (∀x)(Hx ⊃ ~Vx)

(∃x)(Hx • ~Cx) • ~(∀x)(Hx ⊃ Cx)
(∃x)(Hx • Vx) • ~(∀x)(Hx ⊃ (Vx ∨ Cx)]

(∃x)(Hx • Cx) • (∀x)(Hx ⊃ Cx)
(∃x)(Hx • Vx) • ~(∀x)(Hx ⊃ Vx)

(∃x)(Hx • Cx) • ~(∀x)(Hx ⊃ Cx)
(∃x)(Hx • Vx) • ~(∀x)(Hx ⊃ Vx)

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