Question 1

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 2

Every player except Michael is healthy.

Accepted Answer

A)  Pm • ∼Hm • (∃x)(Px • x ≠ m • Hx) 
B)  Pm • ∼Hm • (x)(Px • x ≠ m ⊃ Hx) 
C)  Pm • ∼Hm • (x)[(Px • x ≠ m) ⊃ Hx] 
D)  (x)(Px • ∼Hx • x ≠ m) ⊃ ∼Hm 
E)  (∃x)(Px • ∼Hx • x ≠ m) ⊃ (Pm • ∼Hm) 
A)  Pm • ∼Hm • (∃x)(Px • x ≠ m • Hx) 
B)  Pm • ∼Hm • (x)(Px • x ≠ m ⊃ Hx) 
C)  Pm • ∼Hm • (x)[(Px • x ≠ m) ⊃ Hx] 
D)  (x)(Px • ∼Hx • x ≠ m) ⊃ ∼Hm 
E)  (∃x)(Px • ∼Hx • x ≠ m) ⊃ (Pm • ∼Hm)

Question 3

The father of Angelo is an Italian.

Accepted Answer

A)  (x){[Fxa • (y)(Fya ⊃ y = x)] ⊃ Ix} 
B)  (∃x)(Fxa • Ix) 
C)  (∃x)[Fxa • (y)(Fya ⊃ y = x) • Ix] 
D)  (∃x)[Fxa • (y)(Fya ⊃ y = x)] ⊃ (∃x)Ix 
E)  (x)(Fxa ⊃Ix) 
A)  (x){[Fxa • (y)(Fya ⊃ y = x)] ⊃ Ix} 
B)  (∃x)(Fxa • Ix) 
C)  (∃x)[Fxa • (y)(Fya ⊃ y = x) • Ix] 
D)  (∃x)[Fxa • (y)(Fya ⊃ y = x)] ⊃ (∃x)Ix 
E)  (x)(Fxa ⊃Ix)

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

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 6

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 7

Every giant sequoia is precious.

Accepted Answer

A)  (x)[(Gx ⊃Px) • (Sx ⊃ Px)] 
B)  (x)[(Gx • Sx) ⊃ Px] 
C)  (x)[(Gx ∨Sx) ⊃Px] 
D)  (x)[Px ⊃ (Gx • Sx)] 
E)  (∃x)[Gx • Sx) • Px] 
A)  (x)[(Gx ⊃Px) • (Sx ⊃ Px)] 
B)  (x)[(Gx • Sx) ⊃ Px] 
C)  (x)[(Gx ∨Sx) ⊃Px] 
D)  (x)[Px ⊃ (Gx • Sx)] 
E)  (∃x)[Gx • Sx) • Px]

Question 8

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 9

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 10

Alice will cheer if either Casey or Enright scores a touchdown.

Accepted Answer

A)  Ca ⊃ (Sc ∨ Se) 
B)  (Sc ∨Se) ⊃ Ca 
C)  (Cs ∨ Es) ⊃ Ac 
D)  Ac ⊃ (Cs ∨ Es) 
E)  (∃x)(Cx ∨ Ex) ⊃ (∃y)Ax 
A)  Ca ⊃ (Sc ∨ Se) 
B)  (Sc ∨Se) ⊃ Ca 
C)  (Cs ∨ Es) ⊃ Ac 
D)  Ac ⊃ (Cs ∨ Es) 
E)  (∃x)(Cx ∨ Ex) ⊃ (∃y)Ax

Question 11

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 12

The only victim who survived is Oliver.

Accepted Answer

A)  Vo • So • (x)[(Vx • Sx) ⊃ x = o] 
B)  (Vo • So) ⊃ (x)[(Vx • Sx) ⊃ x = o] 
C)  (x)[(Vx • Sx) ⊃ x = o] 
D)  (∃x)[(Vx • Sx) • x = o] 
E)  (∃x)(Vx • Sx) ⊃ (x)(x = o) 
A)  Vo • So • (x)[(Vx • Sx) ⊃ x = o] 
B)  (Vo • So) ⊃ (x)[(Vx • Sx) ⊃ x = o] 
C)  (x)[(Vx • Sx) ⊃ x = o] 
D)  (∃x)[(Vx • Sx) • x = o] 
E)  (∃x)(Vx • Sx) ⊃ (x)(x = o)

Question 13

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 14

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]

Question 15

Every person trusts someone or other.

Accepted Answer

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

Question 16

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 17

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 18

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 19

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 20

If either Ann or Charlie wins the lottery, then George will celebrate.

Accepted Answer

A)  (x)(Ax ∨Cx) ⊃ Gx 
B)  (Wa ∨Wc) ⊃ Cg 
C)  (Wa • Wc) ⊃ Cg 
D)  (∃x)[(Ax ∨ Cx) • Gx] 
E)  (x)[(Wa ∨Wc) ⊃Cg] 
A)  (x)(Ax ∨Cx) ⊃ Gx 
B)  (Wa ∨Wc) ⊃ Cg 
C)  (Wa • Wc) ⊃ Cg 
D)  (∃x)[(Ax ∨ Cx) • Gx] 
E)  (x)[(Wa ∨Wc) ⊃Cg]

Angela wrote a poem.

Every player except Michael is healthy.

The father of Angelo is an Italian.

Elms and maples are deciduous trees.

A few dogs chase every cat they see.

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

Every giant sequoia is precious.

Some children lose every toy they own.

The only daughter Robert has is Esther.

Alice will cheer if either Casey or Enright scores a touchdown.

A few scholarships were awarded.

The only victim who survived is Oliver.

There is a lamp in the bedroom.

Melinda read a novel.

Every person trusts someone or other.

If any house burns, then every fireman will respond.

Everyone fears someone (or other).

Whoever rides horses is adventurous.

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

If either Ann or Charlie wins the lottery, then George will celebrate.

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

Angela wrote a poem.

Every player except Michael is healthy.

The father of Angelo is an Italian.

Elms and maples are deciduous trees.

A few dogs chase every cat they see.

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

Every giant sequoia is precious.

Some children lose every toy they own.

The only daughter Robert has is Esther.

Alice will cheer if either Casey or Enright scores a touchdown.

A few scholarships were awarded.

The only victim who survived is Oliver.

There is a lamp in the bedroom.

Melinda read a novel.

Every person trusts someone or other.

If any house burns, then every fireman will respond.

Everyone fears someone (or other).

Whoever rides horses is adventurous.

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

If either Ann or Charlie wins the lottery, then George will celebrate.

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