Question 1

The biggest dog in the show is Rover.

Accepted Answer

A)  Dr • Sr • (x)[(Dx • Sx • Brx) ⊃ x ≠ r] 
B)  Dr • Sr • (x)[(Dx • Sx) ⊃ Brx] 
C)  (x)[(Dx • Sx • x ≠ r) ⊃ Brx] 
D)  Dr • Sr • (x)[(Dx • Sx • x ≠ r) ⊃ Brx] 
E)  (x)[(Dx • Sx) ⊃ Brx] 
A)  Dr • Sr • (x)[(Dx • Sx • Brx) ⊃ x ≠ r] 
B)  Dr • Sr • (x)[(Dx • Sx) ⊃ Brx] 
C)  (x)[(Dx • Sx • x ≠ r) ⊃ Brx] 
D)  Dr • Sr • (x)[(Dx • Sx • x ≠ r) ⊃ Brx] 
E)  (x)[(Dx • Sx) ⊃ Brx] D

Question 2

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] E

Question 3

Susan's mother is Chris Campbell.

Accepted Answer

A)  (∃x)(Mxs • x = c) 
B)  (∃x){Mxs • (y)[(Mys ⊃ y = x) ⊃ x = c]} 
C)  (x)(Mxs ⊃ x = c) 
D)  (∃x)[Mxs • (y)(Mys ⊃ y = x) • x = c] 
E)  (x){Mxs ⊃(y)[(Mys ⊃ y = x) • x = c]} 
A)  (∃x)(Mxs • x = c) 
B)  (∃x){Mxs • (y)[(Mys ⊃ y = x) ⊃ x = c]} 
C)  (x)(Mxs ⊃ x = c) 
D)  (∃x)[Mxs • (y)(Mys ⊃ y = x) • x = c] 
E)  (x){Mxs ⊃(y)[(Mys ⊃ y = x) • x = c]} D

Question 4

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 5

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 6

Whoever rides horses is adventurous.

Accepted Answer

A)  (x){Px • (∃y)[(Hy • Rxy) ⊃ Ax]} 
B)  (x){[Px • (∃y)[(Hy • Rxy)] ⊃ Ax} 
C)  (x){[Px • (y)[(Hy • Rxy)] ⊃ Ax} 
D)  (∃x)(Px • Rxh) ⊃ (∃y)Ay 
E)  (x)Px ⊃ (∃y)[(Hy • Rxy) ⊃ Ax] 
A)  (x){Px • (∃y)[(Hy • Rxy) ⊃ Ax]} 
B)  (x){[Px • (∃y)[(Hy • Rxy)] ⊃ Ax} 
C)  (x){[Px • (y)[(Hy • Rxy)] ⊃ Ax} 
D)  (∃x)(Px • Rxh) ⊃ (∃y)Ay 
E)  (x)Px ⊃ (∃y)[(Hy • Rxy) ⊃ Ax]

Question 7

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 8

If every witness tells the truth, then none of the guilty defendants will be acquitted.

Accepted Answer

A)  (x){(Wx ⊃ Tx) ⊃ (x)[(Gx • Dx) ⊃ ∼Ax]} 
B)  (x)(Wx ⊃ Tx) ⊃ (∃x)[Gx • (Dx ⊃ ∼Ax)] 
C)  (x)(Wx ⊃ Tx) ⊃ (x)[(Gx • Dx) ⊃ ∼Ax] 
D)  (x){(Wx ⊃ Tx) ⊃ [(Gx • Dx) ⊃ ∼Ax]} 
E)  (∃x)(Wx • Tx) ⊃ (x)[(Gx • Dx) ⊃ ∼Ax] 
A)  (x){(Wx ⊃ Tx) ⊃ (x)[(Gx • Dx) ⊃ ∼Ax]} 
B)  (x)(Wx ⊃ Tx) ⊃ (∃x)[Gx • (Dx ⊃ ∼Ax)] 
C)  (x)(Wx ⊃ Tx) ⊃ (x)[(Gx • Dx) ⊃ ∼Ax] 
D)  (x){(Wx ⊃ Tx) ⊃ [(Gx • Dx) ⊃ ∼Ax]} 
E)  (∃x)(Wx • Tx) ⊃ (x)[(Gx • Dx) ⊃ ∼Ax]

Question 9

Not all tennis players are high strung.

Accepted Answer

A)  (x)(Tx ⊃ ∼Hx) 
B)  (∃x)(Tx ⊃ ∼Hx) 
C)  (∃x)(Tx • ∼Hx) 
D)  (x)(Hx ⊃Tx) 
E)  (x)(Tx • ∼Hx) 
A)  (x)(Tx ⊃ ∼Hx) 
B)  (∃x)(Tx ⊃ ∼Hx) 
C)  (∃x)(Tx • ∼Hx) 
D)  (x)(Hx ⊃Tx) 
E)  (x)(Tx • ∼Hx)

Question 10

If any house burns, then every fireman will respond.

Accepted Answer

A)  (x)(Hx ⊃Bx) ⊃ (∃x)(Fx • Rx) 
B)  (x)[(Hx • Bx) ⊃ (∃y)(Fy • Ry)] 
C)  (∃x)(Hx • Bx) ⊃ (x)(Fx ⊃ Rx) 
D)  (x)(Hx ⊃Bx) ⊃ (∃x)(Fx • Rx).. 
E)  (x)[(Hx • Bx) ⊃ (Fx • Rx)] 
A)  (x)(Hx ⊃Bx) ⊃ (∃x)(Fx • Rx) 
B)  (x)[(Hx • Bx) ⊃ (∃y)(Fy • Ry)] 
C)  (∃x)(Hx • Bx) ⊃ (x)(Fx ⊃ Rx) 
D)  (x)(Hx ⊃Bx) ⊃ (∃x)(Fx • Rx).. 
E)  (x)[(Hx • Bx) ⊃ (Fx • Rx)]

Question 11

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 12

Everyone fears someone (or other).

Accepted Answer

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

Question 13

The only daughter Robert has is Esther.

Accepted Answer

A)  (x)(Dxr ⊃ e = e) 
B)  Der • (x)(Dxr ⊃ x = e) 
C)  Der 
D)  Der • (x)(x = e ⊃ Der) 
E)  (∃x)(Dxr • x = e) 
A)  (x)(Dxr ⊃ e = e) 
B)  Der • (x)(Dxr ⊃ x = e) 
C)  Der 
D)  Der • (x)(x = e ⊃ Der) 
E)  (∃x)(Dxr • x = e)

Question 14

None but the experienced drivers are cautious and safe.

Accepted Answer

A)  (x){Dx ⊃[Ex ⊃(Cx • Sx)]} 
B)  (x)[(Ex • Dx) ⊃ (Cx • Sx)] 
C)  (x)[(Cx • Sx) ⊃ (Ex • Dx)] 
D)  (x){Dx ⊃[(Cx • Sx) ⊃ Ex]} 
E)  (∃x)[(Dx • Cx) ⊃ (Ex • Sx)] 
A)  (x){Dx ⊃[Ex ⊃(Cx • Sx)]} 
B)  (x)[(Ex • Dx) ⊃ (Cx • Sx)] 
C)  (x)[(Cx • Sx) ⊃ (Ex • Dx)] 
D)  (x){Dx ⊃[(Cx • Sx) ⊃ Ex]} 
E)  (∃x)[(Dx • Cx) ⊃ (Ex • Sx)]

Question 15

There are exactly two cars in the lot.

Accepted Answer

A)  (∃x)(∃y){Cx • Lx • Cy • Ly • x ≠ y • (z)[(Cz • Lz) ⊃ (z = x ∨ z = y)} 
B)  (∃x)(∃y)(Cx • Lx • Cy • Ly • x ≠ y) 
C)  (x)(∃y){Cx • Lx • Cy • Ly • x ≠ y • (z)[(Cz • Lz) ⊃ (z = x ∨ z = y)} 
D)  (∃x)(∃y)(∃z){Cx • Lx • Cy • Ly • x ≠ y • [(Cz • Lz) ⊃ (z = x ∨ z = y)} 
E)  (x)(y){[Cx • Lx • Cy • Ly • x ≠ y] ⊃ (z)[(Cz • Lz) ⊃ (z = x ∨ z = y)} 
A)  (∃x)(∃y){Cx • Lx • Cy • Ly • x ≠ y • (z)[(Cz • Lz) ⊃ (z = x ∨ z = y)} 
B)  (∃x)(∃y)(Cx • Lx • Cy • Ly • x ≠ y) 
C)  (x)(∃y){Cx • Lx • Cy • Ly • x ≠ y • (z)[(Cz • Lz) ⊃ (z = x ∨ z = y)} 
D)  (∃x)(∃y)(∃z){Cx • Lx • Cy • Ly • x ≠ y • [(Cz • Lz) ⊃ (z = x ∨ z = y)} 
E)  (x)(y){[Cx • Lx • Cy • Ly • x ≠ y] ⊃ (z)[(Cz • Lz) ⊃ (z = x ∨ z = y)}

Question 16

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 17

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 18

Every book in the library is misplaced or checked out.

Accepted Answer

A)  (x)[(Bx • Lx) ⊃ (Mx ∨ Cx)] 
B)  (x)[(Bx ⊃Mx) • (Lx ⊃ Cx)] 
C)  (x)[(Bx ⊃Lx) ⊃(Mx ∨Cx)] 
D)  (x)[(Bx • Lx) • (Mx ∨ Cx)] 
E)  (x)[(Bx ∨Lx) ⊃(Mx • Cx)] 
A)  (x)[(Bx • Lx) ⊃ (Mx ∨ Cx)] 
B)  (x)[(Bx ⊃Mx) • (Lx ⊃ Cx)] 
C)  (x)[(Bx ⊃Lx) ⊃(Mx ∨Cx)] 
D)  (x)[(Bx • Lx) • (Mx ∨ Cx)] 
E)  (x)[(Bx ∨Lx) ⊃(Mx • Cx)]

Question 19

There is a lamp in the bedroom.

Accepted Answer

A)  (∃x)(Lx ⊃ Bx) 
B)  (x)(Lx ⊃Bx) 
C)  (x)(Lx • Bx) 
D)  (∃x)(Lx • Bx) 
E)  (∃x)Lx • (∃x)Bx 
A)  (∃x)(Lx ⊃ Bx) 
B)  (x)(Lx ⊃Bx) 
C)  (x)(Lx • Bx) 
D)  (∃x)(Lx • Bx) 
E)  (∃x)Lx • (∃x)Bx

Question 20

Melinda read a novel.

Accepted Answer

A)  (∃x)(Nx • Rmx) 
B)  (∃x)Nx • (∃x)Rmx 
C)  (x)(Nx ⊃Rmx) 
D)  Rmn 
E)  (∃x)[(Nx • Rx) • Mx] 
A)  (∃x)(Nx • Rmx) 
B)  (∃x)Nx • (∃x)Rmx 
C)  (x)(Nx ⊃Rmx) 
D)  Rmn 
E)  (∃x)[(Nx • Rx) • Mx]

The biggest dog in the show is Rover.

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

Susan's mother is Chris Campbell.

There is at most one winner.

Every person dislikes someone or other.

Whoever rides horses is adventurous.

A freshman is not a sophomore.

If every witness tells the truth, then none of the guilty defendants will be acquitted.

Not all tennis players are high strung.

If any house burns, then every fireman will respond.

A small bird landed on the roof.

Everyone fears someone (or other).

The only daughter Robert has is Esther.

None but the experienced drivers are cautious and safe.

There are exactly two cars in the lot.

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

A few athletes excel in every sport.

Every book in the library is misplaced or checked out.

There is a lamp in the bedroom.

Melinda read a novel.

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

The biggest dog in the show is Rover.

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

Susan's mother is Chris Campbell.

There is at most one winner.

Every person dislikes someone or other.

Whoever rides horses is adventurous.

A freshman is not a sophomore.

If every witness tells the truth, then none of the guilty defendants will be acquitted.

Not all tennis players are high strung.

If any house burns, then every fireman will respond.

A small bird landed on the roof.

Everyone fears someone (or other).

The only daughter Robert has is Esther.

None but the experienced drivers are cautious and safe.

There are exactly two cars in the lot.

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

A few athletes excel in every sport.

Every book in the library is misplaced or checked out.

There is a lamp in the bedroom.

Melinda read a novel.

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