Question 1

A wallaby is a marsupial.

Accepted Answer

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

Question 2

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 3

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 4

Goats and sheep are contented only if they are not hungry.

Accepted Answer

A)  (x){[(Gx • Sx) ⊃ (∼Hx ⊃ Cx)] 
B)  (x){[(Gx ∨Sx) ⊃ (∼Hx ⊃ Cx)] 
C)  (x){∼Hx ⊃ [(Gx ∨ Sx) ⊃ Cx]} 
D)  (x)[(Gx • Sx) ⊃ (Cx ⊃ ∼Hx)] 
E)  (x)[(Gx ∨ Sx) ⊃ (Cx ⊃ ∼Hx)] 
A)  (x){[(Gx • Sx) ⊃ (∼Hx ⊃ Cx)] 
B)  (x){[(Gx ∨Sx) ⊃ (∼Hx ⊃ Cx)] 
C)  (x){∼Hx ⊃ [(Gx ∨ Sx) ⊃ Cx]} 
D)  (x)[(Gx • Sx) ⊃ (Cx ⊃ ∼Hx)] 
E)  (x)[(Gx ∨ Sx) ⊃ (Cx ⊃ ∼Hx)]

Question 5

A raccoon is not a mongoose.

Accepted Answer

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

Question 6

A taxi is waiting.

Accepted Answer

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

Question 7

Every journalist knows how to write.

Accepted Answer

A)  Jx ⊃ Kx 
B)  (∃x)(Jx ⊃ Kx) 
C)  (∃x)Jx ⊃ (∃x)Kx 
D)  (x)(Jx ⊃Kx) 
E)  (∃y)(Jy • Ky) 
A)  Jx ⊃ Kx 
B)  (∃x)(Jx ⊃ Kx) 
C)  (∃x)Jx ⊃ (∃x)Kx 
D)  (x)(Jx ⊃Kx) 
E)  (∃y)(Jy • Ky)

Question 8

Megan is a biologist only if William is an astronomer.

Accepted Answer

A)  Bm ⊃ Aw 
B)  Mb ⊃ Wa 
C)  Aw ⊃ Bm 
D)  (∃x)Bx ⊃ (∃x)Ax 
E)  (x)(Mx ⊃Wx) 
A)  Bm ⊃ Aw 
B)  Mb ⊃ Wa 
C)  Aw ⊃ Bm 
D)  (∃x)Bx ⊃ (∃x)Ax 
E)  (x)(Mx ⊃Wx)

Question 9

Large diamonds are costly if they are not flawed.

Accepted Answer

A)  (∃x){∼Fx ⊃ [Lx ⊃ (Dx • Cx)]} 
B)  (x)[(Lx • Dx) ⊃ (∼Fx ⊃ Cx)] 
C)  (x)[(Lx ∨Dx) ⊃ (∼Fx ⊃ Cx)] 
D)  (x)[(Dx • Cx) ⊃ (∼Fx ⊃ Lx)] 
E)  (x)[(∼Fx ⊃ Cx) ⊃ (Lx • Dx)] 
A)  (∃x){∼Fx ⊃ [Lx ⊃ (Dx • Cx)]} 
B)  (x)[(Lx • Dx) ⊃ (∼Fx ⊃ Cx)] 
C)  (x)[(Lx ∨Dx) ⊃ (∼Fx ⊃ Cx)] 
D)  (x)[(Dx • Cx) ⊃ (∼Fx ⊃ Lx)] 
E)  (x)[(∼Fx ⊃ Cx) ⊃ (Lx • Dx)]

Question 10

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]}

Question 11

If there are any guards, then if none of the prisoners escape, then they will be rewarded.

Accepted Answer

A)  (x){[Gx ⊃(y)(Py ⊃ ∼Ey)] ⊃ Rx} 
B)  (x){Gx ⊃ [(∃y)(Py • ∼Ey) ⊃ Rx]} 
C)  (∃x)Gx ⊃ [(y)(Py ⊃ ∼Ey) ⊃ Rx] 
D)  (x){Gx ⊃ [(y)(Py ⊃ ∼Ey) ⊃ Rx]} 
E)  (∃x){Gx • [(y)(Py ⊃ ∼Ey) ⊃ Rx]} 
A)  (x){[Gx ⊃(y)(Py ⊃ ∼Ey)] ⊃ Rx} 
B)  (x){Gx ⊃ [(∃y)(Py • ∼Ey) ⊃ Rx]} 
C)  (∃x)Gx ⊃ [(y)(Py ⊃ ∼Ey) ⊃ Rx] 
D)  (x){Gx ⊃ [(y)(Py ⊃ ∼Ey) ⊃ Rx]} 
E)  (∃x){Gx • [(y)(Py ⊃ ∼Ey) ⊃ Rx]}

Question 12

No liberals are conservatives.

Accepted Answer

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

Question 13

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 14

All the cakes and pies are delicious.

Accepted Answer

A)  (x)[Dx ⊃(Cx ∨Px)] 
B)  (∃x)[(Px • Cx) • Dx] 
C)  (x)[(Cx • Px) ⊃ Dx] 
D)  (x)[(Cx ∨Px) ⊃Dx] 
E)  (∃x)[(Px • Cx) ⊃ Dx] 
A)  (x)[Dx ⊃(Cx ∨Px)] 
B)  (∃x)[(Px • Cx) • Dx] 
C)  (x)[(Cx • Px) ⊃ Dx] 
D)  (x)[(Cx ∨Px) ⊃Dx] 
E)  (∃x)[(Px • Cx) ⊃ Dx]

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

Miriam will be hired if and only if every manager approves.

Accepted Answer

A)  Hm ≡ (∃x)(Mx • Ax) 
B)  Hm ≡ (∃x)(Mx ⊃Ax) 
C)  Hm ≡ (x)(Ax ⊃ Mx) 
D)  Hm ⊃ (x)(Mx ⊃ Ax) 
E)  Hm ≡ (x)(Mx ⊃ Ax) 
A)  Hm ≡ (∃x)(Mx • Ax) 
B)  Hm ≡ (∃x)(Mx ⊃Ax) 
C)  Hm ≡ (x)(Ax ⊃ Mx) 
D)  Hm ⊃ (x)(Mx ⊃ Ax) 
E)  Hm ≡ (x)(Mx ⊃ Ax)

Question 17

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]

Question 18

Ivan will be sad if and only if any child is injured.

Accepted Answer

A)  Si ≡ (∃x)(Cx • Ix) 
B)  (x)[(Cx • Ix) ≡ Ix] 
C)  (∃x)(Cx • Ix) ⊃ Si 
D)  Si ≡ (x)(Cx • Ix) 
E)  Si ≡ (x)(Cx ⊃ Ix) 
A)  Si ≡ (∃x)(Cx • Ix) 
B)  (x)[(Cx • Ix) ≡ Ix] 
C)  (∃x)(Cx • Ix) ⊃ Si 
D)  Si ≡ (x)(Cx • Ix) 
E)  Si ≡ (x)(Cx ⊃ Ix)

Question 19

Every city except Edenville was flooded.

Accepted Answer

A)  (x)[(Cx • x ≠ e) ⊃ Fx] 
B)  Ce • ∼Fe • (x)[(Cx • x ≠ e) ⊃ Fx] 
C)  (Ce • ∼Fe) ⊃(x)[(Cx • x ≠ e) ⊃ Fx] 
D)  Ce • ∼Fe • (∃x)[(Cx • x ≠ e) • Fx] 
E)  Ce • ∼Fe • (x)[(Cx • Fx) ⊃ x ≠ e] 
A)  (x)[(Cx • x ≠ e) ⊃ Fx] 
B)  Ce • ∼Fe • (x)[(Cx • x ≠ e) ⊃ Fx] 
C)  (Ce • ∼Fe) ⊃(x)[(Cx • x ≠ e) ⊃ Fx] 
D)  Ce • ∼Fe • (∃x)[(Cx • x ≠ e) • Fx] 
E)  Ce • ∼Fe • (x)[(Cx • Fx) ⊃ x ≠ e]

Question 20

If all the landscapers are competent, then if none of the roses die, then they will get a bonus.

Accepted Answer

A)  (∃x)(Lx • Cx) ⊃ [(y)(Ry ⊃ ∼Dy) ⊃ Gx] 
B)  (x){(Lx • Cx) ⊃ [(y)(Ry ⊃ ∼Dy) ⊃ Gx]} 
C)  (x){(Lx ⊃Cx) ⊃[(y)(Ry ⊃ ∼Dy) ⊃ Gx]} 
D)  (x)(Lx ⊃ Cx) ⊃[(y)(Ry ⊃ ∼Dy) ⊃ Gx] 
E)  (x)(Lx ⊃Cx) ⊃(y)[(Ry ⊃ ∼Dy) ⊃ Gy] 
A)  (∃x)(Lx • Cx) ⊃ [(y)(Ry ⊃ ∼Dy) ⊃ Gx] 
B)  (x){(Lx • Cx) ⊃ [(y)(Ry ⊃ ∼Dy) ⊃ Gx]} 
C)  (x){(Lx ⊃Cx) ⊃[(y)(Ry ⊃ ∼Dy) ⊃ Gx]} 
D)  (x)(Lx ⊃ Cx) ⊃[(y)(Ry ⊃ ∼Dy) ⊃ Gx] 
E)  (x)(Lx ⊃Cx) ⊃(y)[(Ry ⊃ ∼Dy) ⊃ Gy]

A wallaby is a marsupial.

Not all tennis players are high strung.

None but the experienced drivers are cautious and safe.

Goats and sheep are contented only if they are not hungry.

A raccoon is not a mongoose.

A taxi is waiting.

Every journalist knows how to write.

Megan is a biologist only if William is an astronomer.

Large diamonds are costly if they are not flawed.

Susan's mother is Chris Campbell.

If there are any guards, then if none of the prisoners escape, then they will be rewarded.

No liberals are conservatives.

Every book in the library is misplaced or checked out.

All the cakes and pies are delicious.

There are exactly two cars in the lot.

Miriam will be hired if and only if every manager approves.

The biggest dog in the show is Rover.

Ivan will be sad if and only if any child is injured.

Every city except Edenville was flooded.

If all the landscapers are competent, then if none of the roses die, then they will get a bonus.

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

A wallaby is a marsupial.

Not all tennis players are high strung.

None but the experienced drivers are cautious and safe.

Goats and sheep are contented only if they are not hungry.

A raccoon is not a mongoose.

A taxi is waiting.

Every journalist knows how to write.

Megan is a biologist only if William is an astronomer.

Large diamonds are costly if they are not flawed.

Susan's mother is Chris Campbell.

If there are any guards, then if none of the prisoners escape, then they will be rewarded.

No liberals are conservatives.

Every book in the library is misplaced or checked out.

All the cakes and pies are delicious.

There are exactly two cars in the lot.

Miriam will be hired if and only if every manager approves.

The biggest dog in the show is Rover.

Ivan will be sad if and only if any child is injured.

Every city except Edenville was flooded.

If all the landscapers are competent, then if none of the roses die, then they will get a bonus.

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