Section 5.05 Self-Quiz

. Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. a=b ⊃ c=d
2. Pc • ~Pd

b=d ⊃ a=d

Pd • ~Pc

a=b

c≠d

b=a ⊃ c=d

. Which of the following propositions is derivable from the given premises in F?
1. a=b ⊃ c=d
2. Pc • ~Pd

Pd

a≠b

c=d

b=a

~Pc

. Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∀x)[(Fx • Gx) ⊃ x=e]
2. Fg • g≠e

(Fe • Gg) ⊃ e=e

g=e

(Fg • Gg) ⊃ g=e

(Fx • Gx) ⊃ e=e

(Fx • Gg) ⊃ g=e

. Which of the following propositions is derivable from the given premises in F?
1. (∀x)[(Fx • Gx) ⊃ x=e]
2. Fg • g≠e

(∀x)x=e

Fg • Gg

~Gg

(∃x)(x=g • Gx)

(∃x)(x≠g • Gx)

. Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (Hn • ~In) • (∀x)[(Hx • x≠n) ⊃ Ix]
2. Jn • ~Jo
3. Ho

(Hx • x≠n) ⊃ Ix

Hn • ~In

(Hn • n≠n) ⊃ In

Ho • ~Jo

(Ho • o≠n) ⊃ Io

. Which of the following propositions is derivable from the given premises in F?
1. (Hn • ~In) • (∀x)[(Hx • x≠n) ⊃ Ix]
2. Jn • ~Jo
3. Ho

Io

~(∃x)Ix

x=n

(∀x)[(Hx • x≠o) ⊃ Ix]

(∀x)[Ix ⊃ (Hx • x≠n)]

. Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (Ae • Be) • (Af • ~Bf)
2. (∀x)(Ax ⊃ Dx)

Ae ⊃ De

Af • Ae

~Bf • Be

Ax ⊃ Df

Af ⊃ De

. Which of the following propositions is derivable from the given premises in F?
1. (Ae • Be) • (Af • ~Bf)
2. (∀x)(Ax ⊃ Dx)

(∀x)[Ax ⊃ (x=e ∨ x=f)]

e=f

(∀x)(∀y)[(Dx • Dy) ⊃ x=y]

(∃x)(∃y)(Dx • Dy • x≠y)

(∀x)[(Dx • Bx) ⊃ x=e]

. Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∀x)(∀y)[(Dx • Ex • Dy • Ey) ⊃ y=x]
2. Da • Ea
3. Db • Eb

Da • Db

Ea • Eb

(∀y)[(Dx • Ex • Dy • Ey) ⊃ y=z]

(∀y)[(Da • Ea • Dy • Ey) ⊃ y=a]

(Da • Ea • Db • Eb) ⊃ b=a

.

Which of the following propositions is derivable from the given premises in F?

1. (∀x)(∀y)[(Dx • Ex • Dy • Ey) ⊃ y=x]

2. Da • Ea<br>3. Db • Eb

(∀x)(∀y)x=y

(∀x)(Dx ⊃ Ex)

(∀x)(Ex ⊃ Dx)

(∃x)(∃y)x≠y

a=b

. Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∃x)(∃y)(Ax • Ay • x≠y)
2. (∀x)(Ax ⊃ Bxc)

Ax ⊃ Bcc

(∃y)(Ae • Ay • e≠y)

(∃y)(Ax • Ay • x≠y)

Ac ⊃ Bxc

(∃y)(Ac • Ay • c≠y)

. Which of the following propositions is derivable from the given premises in F?
1. (∃x)(∃y)(Ax • Ay • x≠y)
2. (∀x)(Ax ⊃ Bxc)

~(∃x)(∃y)(Bxc • Byc)

(∀x)(Ax ⊃ Bcx)

(∃x)(∃y)(Bxc • Byc • x≠y)

(∀x)(∃y)(Bxy ⊃ x≠c)

Bcc

. Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∃x)[Nx • (∀y)(Ny ⊃ y=x) • Ox]
2. (∀x)(Ox ⊃ Mx)
3. Nf

Nf • (∀y)(Ny ⊃ y=f) • Of

Of

Ne • (∀y)(Ny ⊃ y=e) • Oe

Ox ⊃ My

Nx • (∀y)(Ny ⊃ y=x) • Ox

. Which of the following propositions is derivable from the given premises in F?
1. (∃x)[Nx • (∀y)(Ny ⊃ y=x) • Ox]
2. (∀x)(Ox ⊃ Mx)
3. Nf

Of

(∀x)(Ox ⊃ Nx)

(∀x)(Ox ⊃ x=f)

(∀x)(Mx ⊃ x=f)

~Mf

. Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∃x){Px • Qx • (∀y)[(Py • Qy) ⊃ y=x] • x=e}
2. Rej • Rek
3. Sj • ~Sk

Pk • Qk • (∀y)[(Py • Qy) ⊃ y=k] • k=e

Ph • Qh • (∀y)[(Py • Qy) ⊃ y=h] • h=e

~Sk • Rek

Px • Qx • (∀y)[(Py • Qy) ⊃ y=x] • x=e

Pe • Qe • (∀y)[(Py • Qy) ⊃ y=e] • e=e

. Which of the following propositions is derivable from the given premises in F?
1. (∃x){Px • Qx • (∀y)[(Py • Qy) ⊃ y=x] • x=e}
2. Rej • Rek
3. Sj • ~Sk

~Pk • ~Qk

(∀x)(∃y)(Rxy ⊃ x=e)

Se

(∃x)[Px • Qx • (∃y)(∃z)(Rxy • Rxz • y≠z)]

~Ree

. Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∃x)(∃y){Kx • Lx • Ky • Ly • x≠y • (∀z)[(Kz • Lz) ⊃ (z=x ∨ z=y)]}
2. (∀x)(Kx ⊃ Mxa)

Ka • La • Kb • Lb • a≠b • (∀z)[(Kz • Lz) ⊃ (z=a ∨ z=b)]

Kb ⊃ Mxa

Ka ⊃ Maa

(∃y){Ka • Lx • Ky • Ly • x≠y • (∀z)[(Kz • Lz) ⊃ (z=a ∨ z=y)]}

(∃y){Kx • La • Ky • Ly • a≠y • (∀z)[(Kz • Lz) ⊃ (z=x ∨ z=y)]}

. Which of the following propositions is derivable from the given premises in F?
1. (∃x)(∃y){Kx • Lx • Ky • Ly • x≠y • (∀z)[(Kz • Lz) ⊃ (z=x ∨ z=y)]}
2. (∀x)(Kx ⊃ Mxa)

(∀x)[(Kx • Lx) ≡ x=a]

(∃x)(Lx • Mxa)

Ka • La

~Maa

(∀x)(Lx ⊃ x=a)

. Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
1. (∃x)(∃y)(∃z){Ax • Ay • Az • Dxe • Dye • Dze • x≠y • x≠z • y≠z • (∀w)[(Aw • Dwe) ⊃ (w=x ∨ w=y ∨ w=z)]}
2. (∀x)(Ax ⊃ Bx)
3. (∀x)(Dxe ⊃ Cx)

(∃y)(∃z){Ab • Ay • Az • Dbe • Dye • Dze • b≠y • b≠z • y≠z • (∀w)[(Aw • Dwe) ⊃ (w=b ∨ w=y ∨ w=z)]}

Ab • Ac • Ad • Dbe • Dce • Dde • b≠c • b≠d • c≠d • (∀w)[(Aw • Dwe) ⊃ (w=b ∨ w=c ∨ w=d)]}

Ab • Ab • Ab • Dbe • Dbe • Dbe • b≠b • b≠b • b≠b • (∀w)[(Aw • Dwe) ⊃ (w=b ∨ w=b ∨ w=b)]}

(∃y)(∃z){Ax • Ay • Az • Dxe • Dye • Dze • x≠y • x≠z • y≠z • (∀w)[(Aw • Dwe) ⊃ (w=x ∨ w=y ∨ w=z)]}

(∃y)(∃z){Ae • Ay • Az • Dee • Dye • Dze • e≠y • e≠z • y≠z • (∀w)[(Aw • Dwe) ⊃ (w=e ∨ w=y ∨ w=z)]}

. Which of the following propositions is derivable from the given premises in F?
1. (∃x)(∃y)(∃z){Ax • Ay • Az • Dxe • Dye • Dze • x≠y • x≠z • y≠z • (∀w)[(Aw • Dwe) ⊃ (w=x ∨ w=y ∨ w=z)]}
2. (∀x)(Ax ⊃ Bx)
3. (∀x)(Dxe ⊃ Cx)

(∀x)(Bx ≡ Cx)

Ae • Be • Dee • Ce

(∃x)(∃y){Bx • Cx • By • Cy • (∀z)[(Bz • Cz) ⊃ (z=x ∨ z=y)]}

(∀x)(∀y)(∀z)(∀w)[(Bx • By • Bz • Bw • Cx • Cy • Cz • Cw) ⊃ (x=y ∨ x=z ∨ x=w ∨ y=z ∨ y=w ∨ z=w)]

(∃x)(∃y)(∃z)(Bx • Cx • By • Cy • Bz • Cz • x≠y • x≠z • y≠z)

Quiz Content