Question 1

If all the plumbers are skilled, then if none of the faucets leak, then they will be commended.

Accepted Answer

A)  (x){(Px • Sx) ⊃ [(y)(Fy ⊃ ∼Ly) ⊃ Cx]} 
B)  (∃x)(Px • Sx) ⊃ [(y)(Fy ⊃ ∼Ly) ⊃ Cy] 
C)  (x)(Px • Sx) ⊃ [(y)(Fy ⊃ ∼Ly) ⊃ Cx] 
D)  (x){(Px ⊃Sx) ⊃[(y)(Fy ⊃ ∼Ly) ⊃ Cx]} 
E)  (x){(Px • Sx) ⊃ [(∃y)(Fy • ∼Ly) ⊃ Cx]} 
A)  (x){(Px • Sx) ⊃ [(y)(Fy ⊃ ∼Ly) ⊃ Cx]} 
B)  (∃x)(Px • Sx) ⊃ [(y)(Fy ⊃ ∼Ly) ⊃ Cy] 
C)  (x)(Px • Sx) ⊃ [(y)(Fy ⊃ ∼Ly) ⊃ Cx] 
D)  (x){(Px ⊃Sx) ⊃[(y)(Fy ⊃ ∼Ly) ⊃ Cx]} 
E)  (x){(Px • Sx) ⊃ [(∃y)(Fy • ∼Ly) ⊃ Cx]} D

Question 2

Every accountant will be dismissed if any of the books has been fixed.

Accepted Answer

A)  (x)(Ax ⊃Dx) ⊃ (∃x)(Bx • Fx) 
B)  (x)[Bx • Fx] ⊃ (Ax ⊃ Dx)] 
C)  (x)[(Bx • Fx) ⊃ (Ax ⊃ Dx)] 
D)  (∃x)(Bx • Fx) ⊃ (x)(Ax ⊃ Dx) 
E)  (∃x)[(Bx • Fx) ⊃ (x)(Ax ⊃ Dx)] 
A)  (x)(Ax ⊃Dx) ⊃ (∃x)(Bx • Fx) 
B)  (x)[Bx • Fx] ⊃ (Ax ⊃ Dx)] 
C)  (x)[(Bx • Fx) ⊃ (Ax ⊃ Dx)] 
D)  (∃x)(Bx • Fx) ⊃ (x)(Ax ⊃ Dx) 
E)  (∃x)[(Bx • Fx) ⊃ (x)(Ax ⊃ Dx)] D

Question 3

Rollins is the shortest player on the team.

Accepted Answer

A)  Pr • (∃x)[(Px • x ≠ r) • Srx] 
B)  Pr • (x)(Srx ⊃ x ≠ r) 
C)  Pr • (x)(Px ⊃ Srx) 
D)  Pr ⊃ (x)[(Px • x ≠ r) ⊃ Srx] 
E)  Pr • (x)[(Px • x ≠ r) ⊃ Srx] 
A)  Pr • (∃x)[(Px • x ≠ r) • Srx] 
B)  Pr • (x)(Srx ⊃ x ≠ r) 
C)  Pr • (x)(Px ⊃ Srx) 
D)  Pr ⊃ (x)[(Px • x ≠ r) ⊃ Srx] 
E)  Pr • (x)[(Px • x ≠ r) ⊃ Srx] E

Question 4

Not every applicant is eligible.

Accepted Answer

A)  (∃x)(Ax • Ex) 
B)  (∃x)Ax • (∃x)∼Ex 
C)  (x)(Ax ⊃ ∼Ex) 
D)  (∃x)(Ax • ∼Ex) 
E)  (x)(Ex ⊃Ax) 
A)  (∃x)(Ax • Ex) 
B)  (∃x)Ax • (∃x)∼Ex 
C)  (x)(Ax ⊃ ∼Ex) 
D)  (∃x)(Ax • ∼Ex) 
E)  (x)(Ex ⊃Ax)

Question 5

Every student except Christopher passed the course.

Accepted Answer

A)  (∃x)[Sx • ∼Px • x = c] 
B)  (Sc • ∼Pc) ⊃(x)[(Sx • Px) ⊃ x ≠ c] 
C)  Sc • ∼Pc • (x)[(Sx • x = c) ⊃ ∼Px] 
D)  (x)[(Sx • ∼Px) ⊃ x = c] 
E)  Sc • ∼Pc • (x)[(Sx • x ≠ c) ⊃ Px] 
A)  (∃x)[Sx • ∼Px • x = c] 
B)  (Sc • ∼Pc) ⊃(x)[(Sx • Px) ⊃ x ≠ c] 
C)  Sc • ∼Pc • (x)[(Sx • x = c) ⊃ ∼Px] 
D)  (x)[(Sx • ∼Px) ⊃ x = c] 
E)  Sc • ∼Pc • (x)[(Sx • x ≠ c) ⊃ Px]

Question 6

Every firefly glows in the dark.

Accepted Answer

A)  (x)(Fx ⊃Gx) 
B)  (x)(Gx ⊃Fx) 
C)  (∃x)(Fx ⊃ Gx) 
D)  (∃x)(Fx • Gx) 
E)  (∃x)(Hx ⊃ Fx) 
A)  (x)(Fx ⊃Gx) 
B)  (x)(Gx ⊃Fx) 
C)  (∃x)(Fx ⊃ Gx) 
D)  (∃x)(Fx • Gx) 
E)  (∃x)(Hx ⊃ Fx)

Question 7

A few athletes excel in every sport.

Accepted Answer

A)  (∃x)[Ax • (Sx ⊃ Ex)] 
B)  (∃x)[Ax • (y)(Sy ⊃ Exy)] 
C)  (x)[Ax ⊃(y)(Sy ⊃ Exy)] 
D)  (∃x)[Ax • (y)Sy ⊃ Exy] 
E)  (∃x)Ax • (y)(Sy ⊃ Exy) 
A)  (∃x)[Ax • (Sx ⊃ Ex)] 
B)  (∃x)[Ax • (y)(Sy ⊃ Exy)] 
C)  (x)[Ax ⊃(y)(Sy ⊃ Exy)] 
D)  (∃x)[Ax • (y)Sy ⊃ Exy] 
E)  (∃x)Ax • (y)(Sy ⊃ Exy)

Question 8

A small bird landed on the roof.

Accepted Answer

A)  (x)[Sx ⊃(Bx ⊃Lx)] 
B)  (x)[(Sx • Bx) ⊃ Lx] 
C)  (∃x)(Sx • Bx) • (∃x)Lx 
D)  (∃x)[(Sx • Bx) • (y) Ly] 
E)  (∃x)[(Sx • Bx) • Lx] 
A)  (x)[Sx ⊃(Bx ⊃Lx)] 
B)  (x)[(Sx • Bx) ⊃ Lx] 
C)  (∃x)(Sx • Bx) • (∃x)Lx 
D)  (∃x)[(Sx • Bx) • (y) Ly] 
E)  (∃x)[(Sx • Bx) • Lx]

Question 9

Not every model is emaciated.

Accepted Answer

A)  (x)(Mx ⊃ ∼Ex) 
B)  (x)∼(Mx ⊃ Ex) 
C)  (∃x)(Mx • ∼Ex) 
D)  ∼(∃x)(Mx • Ex) 
E)  (∃x)(Mx • Ex) 
A)  (x)(Mx ⊃ ∼Ex) 
B)  (x)∼(Mx ⊃ Ex) 
C)  (∃x)(Mx • ∼Ex) 
D)  ∼(∃x)(Mx • Ex) 
E)  (∃x)(Mx • Ex)

Question 10

Every person dislikes someone or other.

Accepted Answer

A)  (x)Px ⊃ (∃y)(Py • Dxy) 
B)  (∃x)[Px • (y)(Py • Dxy)] 
C)  (x)[Px ⊃ (∃y)(Py • Dxy)] 
D)  (∃x)[Px • (∃y)(Py • Dxy)] 
E)  (x)[Px ⊃ (∃y)Py • Dxy] 
A)  (x)Px ⊃ (∃y)(Py • Dxy) 
B)  (∃x)[Px • (y)(Py • Dxy)] 
C)  (x)[Px ⊃ (∃y)(Py • Dxy)] 
D)  (∃x)[Px • (∃y)(Py • Dxy)] 
E)  (x)[Px ⊃ (∃y)Py • Dxy]

Question 11

If Nancy marries Ralph, then everyone in the family will be happy.

Accepted Answer

A)  (Mn • Rm) ⊃ (x)(Fx ⊃ Hx) 
B)  (∃x)(Fx • Hx) ⊃ Mnr 
C)  Mnr ⊃(x)(Fx ⊃ Hx) 
D)  (Nm • Rm) ⊃ (x)(Fx ⊃ Hx) 
E)  Mnr ⊃ (∃x)(Fx ⊃ Hx) 
A)  (Mn • Rm) ⊃ (x)(Fx ⊃ Hx) 
B)  (∃x)(Fx • Hx) ⊃ Mnr 
C)  Mnr ⊃(x)(Fx ⊃ Hx) 
D)  (Nm • Rm) ⊃ (x)(Fx ⊃ Hx) 
E)  Mnr ⊃ (∃x)(Fx ⊃ Hx)

Question 12

There is at most one winner.

Accepted Answer

A)  (∃x)(∃y)(Wx • Wy) 
B)  (x)(y)[(Wx • Wy) ≡ x = y] 
C)  (x)(y)[(Wx • Wy) ⊃ x = y] 
D)  (∃x)(∃y)[(Wx • Wy) • x = y] 
E)  (x)(∃y)[(Wx • Wy) • e = y] 
A)  (∃x)(∃y)(Wx • Wy) 
B)  (x)(y)[(Wx • Wy) ≡ x = y] 
C)  (x)(y)[(Wx • Wy) ⊃ x = y] 
D)  (∃x)(∃y)[(Wx • Wy) • x = y] 
E)  (x)(∃y)[(Wx • Wy) • e = y]

Question 13

A freshman is not a sophomore.

Accepted Answer

A)  Fy ⊃ ∼Sy 
B)  (∃x)(Fx • Sx) 
C)  (∃x)(Fx • ∼Sx) 
D)  Fx • ∼Sx 
E)  (x)(Fx ⊃ ∼Sx) 
A)  Fy ⊃ ∼Sy 
B)  (∃x)(Fx • Sx) 
C)  (∃x)(Fx • ∼Sx) 
D)  Fx • ∼Sx 
E)  (x)(Fx ⊃ ∼Sx)

Question 14

Evans is the fastest runner on the team.

Accepted Answer

A)  Re • Te • (∃x)(Rx • Tx • x ≠ e • Fex] 
B)  Re • Te • (x)[(Rx • Tx • x ≠ e) ⊃ Fex] 
C)  (x)[(Rx • Tx) ⊃ Fex] 
D)  Re • Te • (x)[(Rx • Tx) ⊃ Fex] 
E)  Re • Te • (x)[(Rx • Tx • x = e) ⊃ Fex] 
A)  Re • Te • (∃x)(Rx • Tx • x ≠ e • Fex] 
B)  Re • Te • (x)[(Rx • Tx • x ≠ e) ⊃ Fex] 
C)  (x)[(Rx • Tx) ⊃ Fex] 
D)  Re • Te • (x)[(Rx • Tx) ⊃ Fex] 
E)  Re • Te • (x)[(Rx • Tx • x = e) ⊃ Fex]

Question 15

Only frogs and toads inhabit this cave.

Accepted Answer

A)  (x)[Ix ⊃ (Fx ∨ Tx)] 
B)  (∃x)[(Fx • Tx) ⊃ Ix] 
C)  (x)[Ix ⊃(Fx • Tx)] 
D)  (x)[(Fx • Tx) ⊃ Ix] 
E)  (x)[(Fx ∨ Tx) ⊃ Ix] 
A)  (x)[Ix ⊃ (Fx ∨ Tx)] 
B)  (∃x)[(Fx • Tx) ⊃ Ix] 
C)  (x)[Ix ⊃(Fx • Tx)] 
D)  (x)[(Fx • Tx) ⊃ Ix] 
E)  (x)[(Fx ∨ Tx) ⊃ Ix]

Question 16

Nancy and Raquel will conduct the experiment only if all the young physicists are busy.

Accepted Answer

A)  (Cn • Cr) ⊃ (x)[Bx ⊃ (Yx • Px)] 
B)  (∃x){Cn • Cr • [(Yx • Px) ⊃ Bx]} 
C)  (x)[(Yx • Px) ⊃ Bx] ⊃ (Cn • Cr) 
D)  Nc • Rc • (x)[(Yx • Px) ⊃ Bx] 
E)  (Cn • Cr) ⊃ (x)[(Yx • Px) ⊃ Bx] 
A)  (Cn • Cr) ⊃ (x)[Bx ⊃ (Yx • Px)] 
B)  (∃x){Cn • Cr • [(Yx • Px) ⊃ Bx]} 
C)  (x)[(Yx • Px) ⊃ Bx] ⊃ (Cn • Cr) 
D)  Nc • Rc • (x)[(Yx • Px) ⊃ Bx] 
E)  (Cn • Cr) ⊃ (x)[(Yx • Px) ⊃ Bx]

Question 17

The capital of Arkansas is not Saint Louis.

Accepted Answer

A)  (∃x)(Cxa • x ≠ s) 
B)  (x)(Cxa ⊃ x ≠ s) 
C)  (∃x)[Cxa • (y)(Cya ⊃ x ≠ s)] 
D)  (∃x)[Cxa • (y)(Cya ⊃ y = x) • x ≠ s] 
E)  (∃x)Cxa • ∼Csa 
A)  (∃x)(Cxa • x ≠ s) 
B)  (x)(Cxa ⊃ x ≠ s) 
C)  (∃x)[Cxa • (y)(Cya ⊃ x ≠ s)] 
D)  (∃x)[Cxa • (y)(Cya ⊃ y = x) • x ≠ s] 
E)  (∃x)Cxa • ∼Csa

Question 18

The guests will be happy only if every room is clean and tidy.

Accepted Answer

A)  (∃x)(Gx • Hx) ⊃ (∃x)[Rx ⊃ (Cx • Tx)] 
B)  (x)[Rx ⊃(Cx • Tx)] ⊃ (∃x)(Gx • Hx) 
C)  (∃x)(Gx • Hx) ⊃ (x)[(Rx ⊃ (Cx • Tx)] 
D)  (x){(Gx ⊃ Hx) ⊃[(Rx ⊃(Cx • Tx)]} 
E)  (x)(Gx ⊃Hx) ⊃(x)[(Rx ⊃ (Cx • Tx)] 
A)  (∃x)(Gx • Hx) ⊃ (∃x)[Rx ⊃ (Cx • Tx)] 
B)  (x)[Rx ⊃(Cx • Tx)] ⊃ (∃x)(Gx • Hx) 
C)  (∃x)(Gx • Hx) ⊃ (x)[(Rx ⊃ (Cx • Tx)] 
D)  (x){(Gx ⊃ Hx) ⊃[(Rx ⊃(Cx • Tx)]} 
E)  (x)(Gx ⊃Hx) ⊃(x)[(Rx ⊃ (Cx • Tx)]

Question 19

A mouse is in the closet.

Accepted Answer

A)  (∃x)(Mx ∨ Cx) 
B)  (x)(Mx ⊃Cx) 
C)  (∃x)(Mx ⊃ Cx) 
D)  (x)(Mx • Cx) 
E)  (∃x)(Mx • Cx) 
A)  (∃x)(Mx ∨ Cx) 
B)  (x)(Mx ⊃Cx) 
C)  (∃x)(Mx ⊃ Cx) 
D)  (x)(Mx • Cx) 
E)  (∃x)(Mx • Cx)

Question 20

Some musicians can play every tune they hear.

Accepted Answer

A)  (∃x)Mx • [(y)(Ty • Hxy) ⊃ Pxy] 
B)  (∃x)[Mx • (y)(Ty • Hxy) ⊃ Pxy] 
C)  (x)Tx ⊃ (∃y)[(My • Hyx) ⊃ Pyx] 
D)  (x){Mx ⊃[(y)(Ty • Hxy) ⊃ Pxy]} 
E)  (∃x){Mx • [(y)(Ty • Hxy) ⊃ Pxy]} 
A)  (∃x)Mx • [(y)(Ty • Hxy) ⊃ Pxy] 
B)  (∃x)[Mx • (y)(Ty • Hxy) ⊃ Pxy] 
C)  (x)Tx ⊃ (∃y)[(My • Hyx) ⊃ Pyx] 
D)  (x){Mx ⊃[(y)(Ty • Hxy) ⊃ Pxy]} 
E)  (∃x){Mx • [(y)(Ty • Hxy) ⊃ Pxy]}

If all the plumbers are skilled, then if none of the faucets leak, then they will be commended.

Every accountant will be dismissed if any of the books has been fixed.

Rollins is the shortest player on the team.

Not every applicant is eligible.

Every student except Christopher passed the course.

Every firefly glows in the dark.

A few athletes excel in every sport.

A small bird landed on the roof.

Not every model is emaciated.

Every person dislikes someone or other.

If Nancy marries Ralph, then everyone in the family will be happy.

There is at most one winner.

A freshman is not a sophomore.

Evans is the fastest runner on the team.

Only frogs and toads inhabit this cave.

Nancy and Raquel will conduct the experiment only if all the young physicists are busy.

The capital of Arkansas is not Saint Louis.

The guests will be happy only if every room is clean and tidy.

A mouse is in the closet.

Some musicians can play every tune they hear.

Basic Concepts

Language: Meaning and Definition

Informal Fallacies

Categorical Propositions

Categorical Syllogisms

Propositional Logic

Natural Deduction in Propositional Logic

Analogy and Legal and Moral Reasoning

Causality and Mills Methods

Probability

Statistical Reasoning

Hypotheticalscientific Reasoning

Science and Superstition

Filters

Exam 8: Predicate Logic

If all the plumbers are skilled, then if none of the faucets leak, then they will be commended.

Every accountant will be dismissed if any of the books has been fixed.

Rollins is the shortest player on the team.

Not every applicant is eligible.

Every student except Christopher passed the course.

Every firefly glows in the dark.

A few athletes excel in every sport.

A small bird landed on the roof.

Not every model is emaciated.

Every person dislikes someone or other.

If Nancy marries Ralph, then everyone in the family will be happy.

There is at most one winner.

A freshman is not a sophomore.

Evans is the fastest runner on the team.

Only frogs and toads inhabit this cave.

Nancy and Raquel will conduct the experiment only if all the young physicists are busy.

The capital of Arkansas is not Saint Louis.

The guests will be happy only if every room is clean and tidy.

A mouse is in the closet.

Some musicians can play every tune they hear.

Basic Concepts

Language: Meaning and Definition

Informal Fallacies

Categorical Propositions

Categorical Syllogisms

Propositional Logic

Natural Deduction in Propositional Logic

Analogy and Legal and Moral Reasoning

Causality and Mills Methods

Probability

Statistical Reasoning

Hypotheticalscientific Reasoning

Science and Superstition

Filters