Section 4.05 Self Quiz

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∀x)(Ax ⊃ Bx)
2. ~(∀x)(Ax ⊃ ~Cx)

Ax ⊃ ~Cx correct incorrect

~(Ax ⊃ ~Cx) correct incorrect

~(∃x)~(Ax ⊃ ~Cx) correct incorrect

Ax ⊃ Bx correct incorrect

(∃x)(Ax ⊃ ~Cx) correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∀x)(Ax ⊃ Bx)
2. ~(∀x)(Ax ⊃ ~Cx)

(∀x)(Ax • Cx) correct incorrect

(∀x)(Bx • Cx) correct incorrect

(∃x)(Bx • Cx) correct incorrect

(∃x)~Cx correct incorrect

(∀x)~Cx correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∀x)(Dx ⊃ Ex)
2. (∀x)(Fx ⊃ Gx)
3. ~(∀x)(Ex • ~Fx)

Ex • ~Fx correct incorrect

~(∃x)~(Ex • ~Fx) correct incorrect

Da ⊃ Eb correct incorrect

(∃x)~(Ex • ~Fx) correct incorrect

~(Ex • ~Fx) correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∀x)(Dx ⊃ Ex)
2. (∀x)(Fx ⊃ Gx)
3. ~(∀x)(Ex • ~Fx)

(∃x)(Dx • Gx) correct incorrect

(∃x)(Dx • ~Gx) correct incorrect

(∀x) (Dx ⊃ Gx) correct incorrect

(∃x)(Dx ⊃ Gx) correct incorrect

(∀x) (Gx ⊃ Dx) correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∃x)(Hx • Ix) ⊃ (∀x)(Hx ⊃ ~Jx)
2. (∃x)(Hx • Jx)

(Ha • Ia) ⊃ (∀x)(Hx ⊃ ~Jx) correct incorrect

Ha • Ja correct incorrect

(Hx • Ix) ⊃ (Hx ⊃ ~Jx) correct incorrect

Hx • Jx correct incorrect

(Ha • Ia) ⊃ (Ha ⊃ ~Ja) correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∃x)(Hx • Ix) ⊃ (∀x)(Hx ⊃ ~Jx)
2. (∃x)(Hx • Jx)

(∀x)(Hx ⊃ ~Ix) correct incorrect

(∀x)Hx correct incorrect

(∀x)Ix correct incorrect

Ib correct incorrect

(∃x)Ix correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∀x)(Kx ⊃ ~Lx)
2. (∀x)(Kx ⊃ Mx)
3. ~(∀x)[Kx ⊃ (Nx ∨ Ox)]

(∃x)~[Kx ⊃ (Nx ∨ Ox)] correct incorrect

~(∃x)~[Kx ⊃ (Nx ∨ Ox)] correct incorrect

Kx ⊃ (Nx ∨ Ox) correct incorrect

Ka ⊃ (Nb ∨ Oc) correct incorrect

Kb ⊃ ~Lx correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∀x)(Kx ⊃ ~Lx)
2. (∀x)(Kx ⊃ Mx)
3. ~(∀x)[Kx ⊃ (Nx ∨ Ox)]

(∀x)(Nx • Ox) correct incorrect

(∃x)~Kx correct incorrect

(∃x)[(Mx • ~Nx) • ~(Nx ∨ Ox)] correct incorrect

(∀x)~Kx correct incorrect

(∃x)(Nx • ~Mx) correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∃x)[(Px • Qx) • Rx]
2. (∀x)[(Px • Rx) ⊃ Sx]
3. ~(∃x)[(Qx • Sx) • ~Tx)

(Qx • Sx) • ~Tx correct incorrect

(∀x)~[(Qx • Sx) • ~Tx)] correct incorrect

~(∀x)~[(Qx • Sx) • ~Tx)] correct incorrect

~(∃x)[(Px • Rx) ⊃ Sx] correct incorrect

(Px • Qx) • Rx correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∃x)[(Px • Qx) • Rx]
2. (∀x)[(Px • Rx) ⊃ Sx]
3. ~(∃x)[(Qx • Sx) • ~Tx)

(∃x) [(Px • Qx) • ~Tx] correct incorrect

(∃x)[(Px • Qx) ⊃ Tx] correct incorrect

(∃x) [~ (Px • Qx) • Tx] correct incorrect

(∀x) [(Qx • Sx) ⊃ ~Tx] correct incorrect

(∀x) [(Px • Sx) ⊃ ~Tx] correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∀x)(Ax ≡ Bx)
2. (∃x)~Ax
3. ~(∀x)Bx ⊃ ~(∃x)Cx

~(∃x)~Bx ⊃ ~(∃x)Cx correct incorrect

~Ax correct incorrect

Ac ≡ Ba correct incorrect

~(∀x)Bx ⊃ (∀x)~Cx correct incorrect

~(∀x)~Ax correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∀x)(Ax ≡ Bx)
2. (∃x)~Ax
3. ~(∀x)Bx ⊃ ~(∃x)Cx

(∀x)~Cx correct incorrect

(∀x)Ax correct incorrect

(∃x)Cx correct incorrect

Ac correct incorrect

Bc correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∃x)Dx ≡ (∀x)(Cx ⊃ ~Fx)
2. (∀x)[~Ex ⊃ (Cx • Fx)]
3. ~(∀x)Ex

~(∃x)~Ex correct incorrect

~(∀x)~Ex correct incorrect

Dx ≡ (∀x)(Cx ⊃ ~Fx) correct incorrect

~Ex ⊃ (Cn • Fx) correct incorrect

(∃x)~Ex correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∃x)Dx ≡ (∀x)(Cx ⊃ ~Fx)
2. (∀x)[~Ex ⊃ (Cx • Fx)]
3. ~(∀x)Ex

(∀x)~Cx correct incorrect

(∀x)~Dx correct incorrect

(∀x)~Fx correct incorrect

(∀x)Cx correct incorrect

(∀x)Fx correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∀x)(Gx ⊃ Hx) ⊃ (∃x)(Gx • Jx)
2. ~(∃x)(Gx • ~Kx)
3. (∀x)(Kx ⊃ Hx)
4. ~(∃x)(Jx • ~Ix)

Gx • ~Kx correct incorrect

Ga • ~Ka correct incorrect

(∀x)(Gx ⊃ Hx) ⊃ ~(∀x)~(Gx • Jx) correct incorrect

(Gx ⊃ Hx) ⊃ (∃x)(Gx • Jx) correct incorrect

~(∀x)~(Jx • ~Ix) correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∀x)(Gx ⊃ Hx) ⊃ (∃x)(Gx • Jx)
2. ~(∃x)(Gx • ~Kx)
3. (∀x)(Kx ⊃ Hx)
4. ~(∃x)(Jx • ~Ix)

(∃x)~Ix correct incorrect

(∀x)(Gx • Ix) correct incorrect

(∀x)~Jx correct incorrect

(∃x)(Gx • Ix) correct incorrect

(∃x)(~Ix • ~Jx) correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∀x)[Lx ⊃ ~(Mx • Nx)]
2. (∀x)[Ox ⊃ (Lx • Nx)]
3. ~(∀x)(Ox ⊃ Mx) ⊃ ~(∀x)(Px ⊃ Qx)]
4. (∃x)Ox

~(∀x)(Ox ⊃ Mx) ⊃ (∃x)~(Px ⊃ Qx)] correct incorrect

Ox correct incorrect

~(∃x)(Ox ⊃ Mx) ⊃ ~(∀x)~(Px ⊃ Qx)] correct incorrect

(∀x)~(Ox ⊃ Mx) ⊃ ~(∀x)(Px ⊃ Qx)] correct incorrect

La ⊃ ~(Mx • Nx) correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∀x)[Lx ⊃ ~(Mx • Nx)]
2. (∀x)[Ox ⊃ (Lx • Nx)]
3. ~(∀x)(Ox ⊃ Mx) ⊃ ~(∀x)(Px ⊃ Qx)]
4. (∃x)Ox

(∃x)(Px • ~Qx) correct incorrect

(∃x)(Px • Qx) correct incorrect

(∃x)(~Ox • ~Qx) correct incorrect

(∃x)(~Ox • ~Lx) correct incorrect

(∀x)Qx correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∃x)(Ax • Bx) ⊃ (∀x)(Ex ∨ Fx)
2. ~(∀x)(Bx ⊃ Ex)
3. ~(∃x)Fx

Fa correct incorrect

Fx correct incorrect

Bx ⊃ Ex correct incorrect

~(∃x)~(Bx ⊃ Ex) correct incorrect

(∃x)~(Bx ⊃ Ex) correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∃x)(Ax • Bx) ⊃ (∀x)(Ex ∨ Fx)
2. ~(∀x)(Bx ⊃ Ex)
3. ~(∃x)Fx

(∀x)Fx correct incorrect

(∀x)(Bx • ~Ex) correct incorrect

~(∃x)Ax correct incorrect

(∃x)(Bx • ~Ex) correct incorrect

~(∀x)Ax correct incorrect