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Return to Introduction to Formal Logic Student Resources
Section 4.04 Self Quiz
Quiz Content
*
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
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