Section 4.04 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 • Cx)]
2. (∀x)(Bx ≡ ~Cx)

Ax • (Bx • Cx) correct incorrect

Bc ≡ ~Ce correct incorrect

Ad • (Bd • Cd) correct incorrect

Bx ≡ ~Ce correct incorrect

Ab • (Bc • Cd) correct incorrect

* not completed

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

(∃x)(Ax • ~Cx) correct incorrect

(∀x)[Ax • (Bx • Cx)] correct incorrect

(∀x) Ax correct incorrect

(∀x)(~Cx ⊃ Ax) correct incorrect

(∀x)(~ Ax ⊃ ~Cx) correct incorrect

* not completed

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

~Eb ≡ Fa correct incorrect

~Ea ≡ Fx correct incorrect

Ga ⊃ Fx correct incorrect

Dx ⊃ Ea correct incorrect

Dx ⊃ Ex correct incorrect

* not completed

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

(∃x)(Dx ⊃ ~Gx) correct incorrect

(∃x)(Dx ∨ Ex) correct incorrect

(∀x)(Dx • Ex) correct incorrect

(∀x)(Dx ⊃ ~Gx) correct incorrect

(∃x)(Dx ≡ Fx) 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)Jx
2. Ja • Ha

(Hx ⊃ Ix) ≡ (∃x)Jx correct incorrect

Hx ⊃ Ix correct incorrect

(Hx ⊃ Ix) ≡ Jx correct incorrect

Ja correct incorrect

Jx • Hx correct incorrect

* not completed

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

Ia correct incorrect

~Ia correct incorrect

(Hx ⊃ Ix) ≡ Jx correct incorrect

(∀x)Ix 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 ∨ Mx)]
2. (∃x)(Kx • ~Lx)

Kx • ~Lx correct incorrect

Ka ⊃ (Lx ∨ Mx) correct incorrect

Ka • ~Lx correct incorrect

Ka correct incorrect

Kc • ~Lc correct incorrect

* not completed

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

(∃x)(Lx • Mx) correct incorrect

(∃x)(Kx • Mx) correct incorrect

(∀x)(Kx • Mx) correct incorrect

(∀x)(Lx ∨ Mx) correct incorrect

(∀x)Kx correct incorrect

* not completed

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

Qa ∨ Oa correct incorrect

Nx ⊃ Qb correct incorrect

~(Qx ∨ Ox) correct incorrect

Py ≡ Nz correct incorrect

Na ⊃ Qa correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∀x)(Px ≡ Nx)
2. (∀x)(Nx ⊃ Qx)
3. (∃x)~(Qx ∨ Ox)

(∀x)(~Ox • ~Px) correct incorrect

(∃x)(~Ox • ~Px) correct incorrect

(∀x)(Nx ⊃ Ox) correct incorrect

(∃x)(~Nx ⊃ Ox) correct incorrect

(∀x)(~Px ⊃ Ox) correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∃x)(Rx ∨ Sx)
2. (∀x)(Rx ⊃ Tx)
3. (∀x)(Sx ⊃ Ux)
4. (∀x)~Tx

Rx ∨ Sx correct incorrect

Rx ⊃ Tx correct incorrect

Tx correct incorrect

Sa ⊃ Ux correct incorrect

Rx ⊃ Ta correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∃x)(Rx ∨ Sx)
2. (∀x)(Rx ⊃ Tx)
3. (∀x)(Sx ⊃ Ux)
4. (∀x)~Tx

(∀x)Sx correct incorrect

(∃x)Tx correct incorrect

(∃x)Ux correct incorrect

(∃x)Rx correct incorrect

(∀x)Ux correct incorrect

* not completed

. Which of the following propositions is an immediate (one-step) consequence in M of the given premises:
1. (∃x)(Yx • ~Zx)
2. (∀x)(Wx ≡ Xx)
3. (∀x)(~Wx ⊃ Zx)

Yx • ~Zx correct incorrect

~Za correct incorrect

Ws ≡ Xx correct incorrect

Wx ≡ Xx correct incorrect

Ya • ~Zb correct incorrect

* not completed

. Which of the following propositions is derivable from the given premises in M:
1. (∃x)(Yx • ~Zx)
2. (∀x)(Wx ≡ Xx)
3. (∀x)(~Wx ⊃ Zx)

(∃x)(Xx • Yx) correct incorrect

(∀x)(Xx • Yx) correct incorrect

(∀x)~Wx correct incorrect

(∀x)~Zx correct incorrect

(∀x)Yx correct incorrect

* not completed

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

Ab ⊃ (Bb ⊃ Eb) correct incorrect

Bx • ~Dx correct incorrect

Ab ⊃ (∀x)(Bx ⊃ Ex) correct incorrect

Ca ⊃ Db correct incorrect

~Ad ⊃ Cd correct incorrect

* not completed

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

(∃x)(Ax • Cx) correct incorrect

(∃x)(Dx • ~Bx) correct incorrect

(∃x)(Ax • Dx) correct incorrect

(∃x)(Ex • ~Bx) correct incorrect

(∃x)(Ex • ~Dx) correct incorrect

* not completed

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

Fx • ~Gx correct incorrect

(Fx • ~Gs) ⊃ Ix correct incorrect

(Fx • Hx) • ~Gx correct incorrect

(Fa • Ha) • ~Ga correct incorrect

(Hx • Ix) ⊃ Js correct incorrect

* not completed

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

(∀x)Hx correct incorrect

(∀x)~Ix correct incorrect

(∃x)~Fx correct incorrect

(∃x)(Fx • Jx) correct incorrect

(∃x)~Hx 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) ⊃ (∀x)(Kx ⊃ Mx)
2. (∃x)(Kx • Nx)
3. (∀x)[Kx ⊃ (Nx ≡ Lx)]
4. (∃x)[(Kx • Mx) • Ox]

(Kx • Mx) • Ox correct incorrect

(Ka • La) ⊃ (∀x)(Kx ⊃ Mx) correct incorrect

(Km • Mm) • On correct incorrect

Kx ⊃ (Nx ≡ Lx) correct incorrect

Kx • Nx correct incorrect

* not completed

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

(∀x)(Kx ⊃ Lx) correct incorrect

(∀x)(Kx ⊃ Nx) correct incorrect

(∀x)Ox correct incorrect

(∀x)Nx correct incorrect

(∃x)Ox correct incorrect