Question 1

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 2

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]

Question 3

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 4

Elms and maples are deciduous trees.

Accepted Answer

A)  (x)[(Ex ∨Mx) ⊃ (Dx ⊃ Tx)] 
B)  (∃x)[(Ex ∨ Mx) ⊃ (Tx • Dx)] 
C)  (x)[(Ex • Mx) ⊃ (Tx • Dx)] 
D)  (x)[(Ex ∨Mx) ⊃(Tx • Dx)] . 
E)  (∃x)[(Ex ∨ Mx) ⊃ (Tx • Dx)]. 
A)  (x)[(Ex ∨Mx) ⊃ (Dx ⊃ Tx)] 
B)  (∃x)[(Ex ∨ Mx) ⊃ (Tx • Dx)] 
C)  (x)[(Ex • Mx) ⊃ (Tx • Dx)] 
D)  (x)[(Ex ∨Mx) ⊃(Tx • Dx)] . 
E)  (∃x)[(Ex ∨ Mx) ⊃ (Tx • Dx)].

Question 5

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 6

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 7

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 8

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 9

Some children lose every toy they own.

Accepted Answer

A)  (∃x){Cx • (y)[(Ty • Oxy) ⊃ Lxy]} 
B)  (∃x){[Cx • (∃y)(Ty • Oxy)] ⊃ Lxy} 
C)  (x){[Cx • (y)(Ty • Oxy)] ⊃ Lxy} 
D)  (x){[Cx ⊃(y)(Ty • Oxy)] ⊃ Lxy} 
E)  (∃x)[Cx • (y)(Ty • Oxy)] ⊃ (y)Lxy 
A)  (∃x){Cx • (y)[(Ty • Oxy) ⊃ Lxy]} 
B)  (∃x){[Cx • (∃y)(Ty • Oxy)] ⊃ Lxy} 
C)  (x){[Cx • (y)(Ty • Oxy)] ⊃ Lxy} 
D)  (x){[Cx ⊃(y)(Ty • Oxy)] ⊃ Lxy} 
E)  (∃x)[Cx • (y)(Ty • Oxy)] ⊃ (y)Lxy

Question 10

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 11

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)]

Question 12

A few scholarships were awarded.

Accepted Answer

A)  (∃x)(Sx ⊃ Ax) 
B)  (∃x)(Sx • Ax) 
C)  (x)(Sx ⊃Ax) 
D)  Sy • Ay 
E)  (x)(Sx • Ax) 
A)  (∃x)(Sx ⊃ Ax) 
B)  (∃x)(Sx • Ax) 
C)  (x)(Sx ⊃Ax) 
D)  Sy • Ay 
E)  (x)(Sx • Ax)

Question 13

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 14

Angela wrote a poem.

Accepted Answer

A)  (∃x)(Px • Wax) 
B)  (x)(Wax ⊃Px) 
C)  Wap 
D)  (∃x)(∃y)(Px • Wxy) 
E)  (∃x)(Px • Ap) 
A)  (∃x)(Px • Wax) 
B)  (x)(Wax ⊃Px) 
C)  Wap 
D)  (∃x)(∃y)(Px • Wxy) 
E)  (∃x)(Px • Ap)

Question 15

A few dogs chase every cat they see.

Accepted Answer

A)  (∃x){Dx ⊃ (y)[(Cy • Sxy) ⊃ Cxy]} 
B)  (x){Dx ⊃(y)[(Cy • Sxy) ⊃ Cxy]} 
C)  (∃x)Dx • (y)[(Cy • Sxy) ⊃ Cxy] 
D)  (∃x)Dx ⊃ (y)[(Cy • Sxy) ⊃ Cxy 
E)  (∃x){Dx • (y)[(Cy • Sxy) ⊃ Cxy]} 
A)  (∃x){Dx ⊃ (y)[(Cy • Sxy) ⊃ Cxy]} 
B)  (x){Dx ⊃(y)[(Cy • Sxy) ⊃ Cxy]} 
C)  (∃x)Dx • (y)[(Cy • Sxy) ⊃ Cxy] 
D)  (∃x)Dx ⊃ (y)[(Cy • Sxy) ⊃ Cxy 
E)  (∃x){Dx • (y)[(Cy • Sxy) ⊃ Cxy]}

Question 16

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 17

If Andy and Carol pass the test, then Eve will be delighted.

Accepted Answer

A)  (Pa ∨Pc) ⊃ Ed 
B)  (x)Px ⊃ (∃y)Dy 
C)  (Ap • Cp) ⊃ Ed 
D)  Pac ⊃ De 
E)  (Pa • Pc) ⊃ De 
A)  (Pa ∨Pc) ⊃ Ed 
B)  (x)Px ⊃ (∃y)Dy 
C)  (Ap • Cp) ⊃ Ed 
D)  Pac ⊃ De 
E)  (Pa • Pc) ⊃ De

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

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 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]}

Only frogs and toads inhabit this cave.

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

Every firefly glows in the dark.

Elms and maples are deciduous trees.

Not every applicant is eligible.

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

Every student except Christopher passed the course.

All the cakes and pies are delicious.

Some children lose every toy they own.

Every journalist knows how to write.

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

A few scholarships were awarded.

A mouse is in the closet.

Angela wrote a poem.

A few dogs chase every cat they see.

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

If Andy and Carol pass the test, then Eve will be delighted.

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

Evans is the fastest runner on the team.

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

Only frogs and toads inhabit this cave.

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

Every firefly glows in the dark.

Elms and maples are deciduous trees.

Not every applicant is eligible.

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

Every student except Christopher passed the course.

All the cakes and pies are delicious.

Some children lose every toy they own.

Every journalist knows how to write.

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

A few scholarships were awarded.

A mouse is in the closet.

Angela wrote a poem.

A few dogs chase every cat they see.

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

If Andy and Carol pass the test, then Eve will be delighted.

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

Evans is the fastest runner on the team.

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