Section 5.02 Self-Quiz

* not completed

. Consider the following domain, assignment of objects in the domain, and interpretations of predicates.
Domain = {Integers}
a: 0
b: 5
c: 4
d: 2
Ex: x is even
Ox: x is odd
Px: x is a prime number
Gxy: x is greater than y
Given the customary truth tables, which of the following theories is modeled by the above interpretation?

(Ea • Ed) • (Eb • Ec)
Gca • (∃x)Gxd correct incorrect

(Ea • Ed) • (Ob • Ec)
Gba • (∃x)Gxb correct incorrect

(Ea • Od) • (Ob • Ec)
Gda • (∃x)Gbx correct incorrect

(Ea • Ec) • (Ed • Ob)
Gdb • (∃x)Gax correct incorrect

(Ea • Ec) • (Ed • Ob)
Gcb • (∃x)Gac correct incorrect

* not completed

. Consider the following domain, assignment of objects in the domain, and interpretations of predicates.
Domain = {Integers}
a: 0
b: 5
c: 4
d: 2
Ex: x is even
Ox: x is odd
Px: x is a prime number
Gxy: x is greater than y
Given the customary truth tables, which of the following theories is modeled by the above interpretation?

(Gdc • Gbc) • Gca
(∀x)[Ox ⊃ (∃y)(Ey • ~Gyx)] correct incorrect

(Gba • Gbc) ∨ Gda
(∀x)[Ox ⊃ (∃y)(~Ey • Gxy)] correct incorrect

(Gdc • Gda) ∨ Gcb
(∀x)[Ox ⊃ (∃y)(Ey • ~Gxy)] correct incorrect

(Gac • Gad) ∨ Gaa
(∀x)[Ox ⊃ ~(∃y)(Ey • Gxy)] correct incorrect

(Gba • Gda) ∨ Gac
(∀x)[Ox ⊃ (∃y)(Ey • Gyx)] correct incorrect

* not completed

. Consider the following domain, assignment of objects in the domain, and interpretations of predicates.
Domain = {Integers}
a: 0
b: 5
c: 4
d: 2
Ex: x is even
Ox: x is odd
Px: x is a prime number
Gxy: x is greater than y
Given the customary truth tables, which of the following theories is modeled by the above interpretation?

Pc ∨ Pd
(∃x)(Px • Gxd)
(∀x)[Ox ⊃ (∃y)(Py • Gyx)] correct incorrect

Pb ∨ Pd
(∃x)(Px • Gdx)
(∀x)[Ox ⊃ (∃y)(Py • Gxy)] correct incorrect

Pa ∨ Pc
(∃x)(Px • Gxb)
(∀x)[~Ox ⊃ ~(∃y)(Py • Gyx)] correct incorrect

Pa ∨ Pb
(∃x)(Px • Gbx)
(∀x)[Ox ⊃ ~(∃y)(Py • Gxy)] correct incorrect

Pb ∨ Pc
(∃x)(Px • Gax)
(∀x)[~Ox ⊃ (∃y)(Py • Gyx)] correct incorrect

* not completed

. Consider the following domain, assignment of objects in the domain, and interpretations of predicates.
Domain = {Integers}
a: 0
b: 5
c: 4
d: 2
Ex: x is even
Ox: x is odd
Px: x is a prime number
Gxy: x is greater than y
Given the customary truth tables, which of the following theories is modeled by the above interpretation?

~Gcb • Gbc
(∀x)(∃y)Gxy
(∀x)(∀y)(Gxy ⊃ Gyx) correct incorrect

~Gdb • Gbd
(∀x)(∀y)Gxy
(∀x)(∀y)(~Gxy ⊃ Gyx) correct incorrect

~Gba • Gab
(∃x)(∃y)Gxy
(∀x)(∀y)(~Gyx ⊃ Gxy) correct incorrect

~Gab • Gba
(∀x)(∃y)Gyx
(∀x)(∀y)(Gxy ⊃ ∌Gyx) correct incorrect

~Gbd • Gdb
(∃x)(∀y)Gyx
(∀x)(∀y)(Gxy ≡ ~Gyx) correct incorrect

* not completed

. Consider the following domain, assignment of objects in the domain, and interpretations of predicates.
Domain = {Integers}
a: 0
b: 5
c: 4
d: 2
Ex: x is even
Ox: x is odd
Px: x is a prime number
Gxy: x is greater than y
Given the customary truth tables, which of the following theories is modeled by the above interpretation?

(∃x)[(Ex • Px) • ~Gcx]
(∀x)[(Px • Gdx) ⊃ Ex] correct incorrect

(∃x)[(Ox • Px) • ~Gxc]
(∀x)[(Px • Gbx) ⊃ Ox] correct incorrect

(∃x)[(Ox • Px) • ~Gcx]
(∀x)((Px • Gxb) ⊃ Ex] correct incorrect

(∃x)[(Ex • Px) • ∌Gxc]
(∀x)[(Px • Gxd) ⊃ ~Ex] correct incorrect

(∃x)[(Ex • Ox) • ~Gxc]
(∀x)[(Px • Gxb) ⊃ Ox] correct incorrect

* not completed

. Select a counterexample for the given invalid argument.
Aa ∨ (∃x)Bxa / (∃x)Bxx

Counterexample in a domain of a member, in which:
Aa: True     Baa: True correct incorrect

Counterexample in a domain of 2 members, in which:
Aa: False     Baa: False
Bba: False correct incorrect

Counterexample in a domain of 2 members, in which:
Aa: True     Baa: False
Bba: False     Bbb: True correct incorrect

Counterexample in a domain of a member, in which:
Aa: False     Baa: False correct incorrect

Counterexample in a domain of a member, in which:
Aa: True     Baa: False correct incorrect

* not completed

. Select a counterexample for the given invalid argument.
1. (∀x)(Dx ⊃ Exa)
2. (∃x)(Eax • Dx) / (∀x)(Dx ⊃ Eax)

Counterexample in a domain of a member, in which:
Da: True     Eaa: True correct incorrect

Counterexample in a domain of 2 members, in which:
Da: True     Eaa: True
Db: True     Eab: False
Eba: True correct incorrect

Counterexample in a domain of a member, in which:
Da: False     Eaa: False correct incorrect

Counterexample in a domain of 2 members, in which:
Da: True     Eaa: True
Db: False     Eab True correct incorrect

Counterexample in a domain of 2 members, in which:
Da: True     Eaa: False
Db: True     Eab: True
Eba: True correct incorrect

* not completed

. Select a counterexample for the given invalid argument.
1. (∀x)[Hx ⊃ (∃y)(Hy • Ixy)]
2. Ha / Iaa

Counterexample in a domain of a member, in which:
Ha: True     Iaa: False correct incorrect

Counterexample in a domain of 2 members, in which:
Ha: True     Iaa: False     Iba: True
Hb: False     Iab: True     Ibb: True correct incorrect

Counterexample in a domain of 2 members, in which:
Ha: True     Iaa: False     Iba: True
Hb: True     Iab: True     Ibb: True correct incorrect

Counterexample in a domain of 2 members, in which:
Ha: True     Iaa: False     Iba: False
Hb: True     Iab: False     Ibb: True correct incorrect

Counterexample in a domain of 2 members, in which:
Ha: True     Iaa: True     Iba: True
Hb: False     Iab: True     Ibb: False correct incorrect

* not completed

. Select a counterexample for the given invalid argument.
1. (∃x)[Px • (∀y)Qxy]
2. (∃x)[(∃y)Qyx • Rx] / (∀x)(Px ⊃ Rx)

Counterexample in a domain of 2 members, in which:
Pa: True     Qaa: True
Pb: True     Qab: True
Ra: False     Qba: True
Rb: True     Qbb: True correct incorrect

Counterexample in a domain of 2 members, in which:
Pa: True     Qaa: True
Pb: False     Qab: False
Ra: True     Qba: False
Rb: True     Qbb: True correct incorrect

Counterexample in a domain of 2 members, in which:
Pa: False     Qaa: False
Pb: True     Qab: True
Ra: True     Qba: True
Rb: True     Qbb: True correct incorrect

Counterexample in a domain of 2 members, in which:
Pa: False     Qaa: False
Pb: False     Qab: True
Ra: True     Qba: True
Rb: True     Qbb: True correct incorrect

Counterexample in a domain of 2 members, in which:
Pa: True     Qaa: True
Pb: True     Qab: False
Ra: True     Qba: False
Rb: False     Qbb: False correct incorrect

* not completed

. Select a counterexample for the given invalid argument.
1. (∃x)[Dx • (∃y)(Dy • Fyx)]
2. (∀x)(Dx ⊃ Ex) / (∀x)[Ex ⊃ (∃y)(Ey • Fyx)]

Counterexample in a domain of 2 members, in which:
Da: True     Faa: True
Db: True     Fab: False
Ea: False     Fba: True
Eb: False    Fbb: True correct incorrect

Counterexample in a domain of 2 members, in which:
Da: True     Faa: False
Db: False     Fab: False
Ea: True     Fba: True
Eb: False     Fbb: False correct incorrect

Counterexample in a domain of 2 members, in which:
Da: True     Faa: True
Db: True     Fab: True
Ea: True     Fba: True
Eb: True     Fbb: False correct incorrect

Counterexample in a domain of 2 members, in which:
Da: False     Faa: False
Db: True     Fab: True
Ea: False     Fba: False
Eb: False     Fbb: False correct incorrect

Counterexample in a domain of 2 members, in which:
Da: True     Faa: False
Db: True     Fab: False
Ea: True     Fba: False
Eb: True     Fbb: True correct incorrect