Question 1

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 2

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 3

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 4

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 5

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 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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]

Question 15

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]

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

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 18

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]}

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

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

A raccoon is not a mongoose.

Every person trusts someone or other.

Not every model is emaciated.

Every player except Michael is healthy.

The capital of Arkansas is not Saint Louis.

Every giant sequoia is precious.

The only victim who survived is Oliver.

Large diamonds are costly if they are not flawed.

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

A wallaby is a marsupial.

The father of Angelo is an Italian.

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

Megan is a biologist only if William is an astronomer.

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

Rollins is the shortest player on the team.

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

No liberals are conservatives.

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

Every city except Edenville was flooded.

A taxi is waiting.

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 raccoon is not a mongoose.

Every person trusts someone or other.

Not every model is emaciated.

Every player except Michael is healthy.

The capital of Arkansas is not Saint Louis.

Every giant sequoia is precious.

The only victim who survived is Oliver.

Large diamonds are costly if they are not flawed.

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

A wallaby is a marsupial.

The father of Angelo is an Italian.

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

Megan is a biologist only if William is an astronomer.

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

Rollins is the shortest player on the team.

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

No liberals are conservatives.

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

Every city except Edenville was flooded.

A taxi is waiting.

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