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Return to Introduction to Formal Logic Student Resources
Section 5.02 Self-Quiz
Quiz Content
*
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 ⊃ âŒGyx)
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) • âŒGxc]
(∀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
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