Section 5.01 Self-Quiz

. Select the best translation into predicate logic. David teaches Chris. (c: Chris; d: David; Txy: x teaches y)

Tdc

Tcd

Tcc

dTc

cTd

. Select the best translation into predicate logic. Earth isn't bigger than Jupiter. (e: Earth; j: Jupiter; Bxy: x is bigger than y)

~Bje

Bej

Bje~

~Bej

B~ej

. Select the best translation into predicate logic. Holly loves Frances. (f: Frances; h: Holly; Lxy: x loves y)

hLf

fLh

Lfh

Lff

Lhf

. Select the best translation into predicate logic. Leo is taller than Cathy. (c: Cathy; l: Leo; Txy: x is taller than y)

Tlc

Tcl

lTc

cTl

~Tlc

. Select the best translation into predicate logic. Alexis is greeted by Ben. (a: Alexis; b: Ben; Gxy: x greets y)

Gab

~Gba

aGb

Gba

bGa

. Select the best translation into predicate logic.George borrows Hector's lawnmower. (g: George; h: Hector; l: Hector's lawnmower; Bxyx: x borrows y from z)

Blgh

Bhlg

Bglh

Bghl

Bhgl

. Select the best translation into predicate logic. José introduces Wilma to Kevin. (j: José; k: Kevin; w: Wilma; Ixyz: x introduces y to z)

Iwkj

Ijwk

Iwjk

Ijkw

Ikjw

. Select the best translation into predicate logic. Kevin is introduced to José by Wilma. (j: José; k: Kevin; w: Wilma; Ixyz: x introduces y to z)

Iwjk

Ijkw

Ikjw

Ijwk

Iwkj

. Select the best translation into predicate logic. Marco moves from Italy to Spain. (i: Italy; m: Marco; s: Spain; Mxyz: x moves to y from z)

Msim

Mmis

Mims

Msmi

Mmsi

. Select the best translation into predicate logic. Marco doesn't move from Spain to Italy. (i: Italy; m: Marco; s: Spain; Mxyz: x moves to y from z)

~Mmsi

M~mis

~Mmis

M~msi

Mmsi

. Select the best translation into predicate logic. All planets are smaller than Jupiter. (j: Jupiter; Px: x is a planet; Sxy: x is smaller than y)

(∃x)(Px • Sxj)

(∀x)(Px • Sxj)

(∀x)(Px ⊃ Sjx)

(∃x)(Px ⊃ Sxj)

(∀x)(Px ⊃ Sxj)

. Select the best translation into predicate logic. All kings are luckier than all paupers. (Kx: x is a king; Px: x is a pauper; Lxy: x is luckier than y)

(∀x)[Kx ⊃ (∀y)(Py ⊃ Lxy)]

(∀x)[Kx ⊃ (∀y)(Lxy ⊃ Py)]

(∀x)(∀y)[(Kx • Py) ⊃ Lyx]

(∀x)[(Kx • (∀y)(Py)) ⊃ Lxy]

(∀x)[Kx ⊃ (∀x)(Px ⊃ Lxx)]

. Select the best translation into predicate logic. All birds live in some nest. (Bx: x is a bird; Nx: x is a nest; Lxy: x lives in y)

(∀x)(∀y)[(Bx • Ny) ⊃ Lxy]

(∀x)[Bx ⊃ (∃y)(Ny • Lxy)]

(∀x)[(∃y)(Ny • Bx) ⊃ Lxy]

(∀x)(∃y)[(Bx • Ny) ⊃ Lxy]

(∀x)[Bx ⊃ (∀y)(Ny ⊃ Lxy)]

. Select the best translation into predicate logic. Some CEO is wealthier than everyone. (Cx: x is a CEO; Px: x is a person; Wxy: x is wealthier than y)

(∃x)[Cx • (∀y)(Py • Wxy)]

(∃x)[Cx ⊃ (∀y)(Py ⊃ Wxy)]

(∃x)[Cx • (∀y)(Py ⊃ Wxy)]

(∀x)[Px ⊃ (∃y)(Cy ⊃ Wxy)]

(∃x)(∀y)[(Cy • Px) ⊃ Wxy)]

. Select the best translation into predicate logic. All jellybeans are sweeter than all fruit. (Fx: x is a fruit; Jx: x is a jellybean; Sxy: x is sweeter than y)

(∀x)[Fx ⊃ (∀y)(Jy ⊃ Sxy)]

(∀x)(∀y)[(Fx • Jy) • Sxy]

(∀x)(∀y)[Sxy ⊃ (Fy • Jx)]

(∀x)[(Jx ⊃ (∃y)(Fy • Sxy)]

(∀x)[Jx ⊃ (∀y)(Fy ⊃ Sxy)]

. Select the best translation into predicate logic. All children go to some school. (Cx: x is a child; Sx: x is a school; Gxy: x goes to y)

(∀x)(∃y)[(Cx • Sy) • Gxy)

(∀x)[Sx ⊃ (∃y)(Cy • Gxy)]

(∀x)[Cx ⊃ (∃y)(Sy • Gxy)]

(∀x)[Sx • (∃y)(Cy • Gxy)]

(∃x)[Sx • (∀y)(Cy ⊃ Gxy)]

. Select the best translation into predicate logic.Some robbers steal money from a bank. (Bx: x is a bank; Mx: x is money; Rx: x is a robber; Sxyz: x steals y from z)

(∃x){Bx • (∃y)[Ry • (∀z)(Mz ⊃ Syzx)]}

(∃x)(∃y)(∃z)[(Rx • By) • (Mz • Syxz)]

(∃x){Rx ⊃ (∃y)[My ⊃ (∃z)(Bz ⊃ Sxyz)]}

(∃x){Rx • (∃y)[My • (∃z)(Bz • Sxyz)]}

(∃x){Rx • (∃y[My ⊃ (∃z)(Bz • Sxyz)]}

. S Select the best translation into predicate logic. Some kind people help some endangered species. (Ex: x is endangered; Kx: x is kind; Px: x is a person; Sx: x is a species; Hxy: x helps y)

(∃x){(Kx • Px) • (∃y)[(Ey • Sy) • Hxy]}

(∃x)(∃y){[(Kx • Sx) • (Ey • Py)] • Hxy}

(∃x)(∃y){[(Kx • Sx) • (Ey • Py)] • Hyx}

(∃x)(∃y){[(Kx • Px) • (Ey • Sy)] ⊃ Hxy}

(∃x)(∃y){[(Kx • Px) • (Ey • Sy)] ⊃ Hyx}

. Select the best translation into predicate logic. Some animals are neglected by cruel people. (Ax: x is an animal; Cx: x is cruel; Px: x is a person; Nxy: x neglects y)

(∃x)[(Ax • Cx) • (∃y)(Py • Nyx)]

(∃x)[(Cx • Px) • (∃y)(Ay • Nxy)]

(∃x)[(Ax • Px) • (∃y)(Cy • Nxy)]

(∃x)(∃y){[(Ax • Cy) • Py] • Nxy)]}

(∃x)(∃y)[(Cx • Px) ⊃ (Ay • Nxy)]

. Select the best translation into predicate logic. Some firefighters rescue victims from danger. (Dx: x is danger; Fx: x is a firefighter; Vx: x is a victim; Rxyz: x rescues y from z)

(∃x){Fx • (∀y)[Dy ⊃ (∃z)(Vz • Rxyz)]}

(∃x){Fx • (∃y)[Vy • (∃z)(Dz • Rxyz)]}

(∃x){Fx • (∃y)(∃z)[(Vy • Dz) • Rxzy]}

(∀x){Fx ⊃ (∃y)[Vy . (∃z)(Dz • Rxyz)]}

(∀x)(∃y)(∃z){[(Fx • Vy) • Dz] ⊃ Rxyz}

.

Select the best English interpretation of the given proposition, using the following translation key:

Ax: x is an apartment

Hx: x is a house

Lx: x is large

Bxy: x is bigger than y

(∃x)[Hx • (∀y)(Ay ⊃ Bxy)]

Some houses are smaller than all apartments.

Every house is bigger than every apartment.

Some apartment is smaller than every house.

Some houses are bigger than some apartments.

Some houses are bigger than every apartment.

.

Select the best English interpretation of the given proposition, using the following translation key:

Ax: x is an apartment

Hx: x is a house

Lx: x is large

Bxy: x is bigger than y

(∀x)[Ax ⊃ (∃y)(Hy • Bxy)]

Every apartment is bigger than some house.

Every house is bigger than all apartments.

Every house is bigger than some apartment.

Some house is bigger than every apartment.

Every apartment is bigger than every house.

.

Select the best English interpretation of the given proposition, using the following translation key:

Ax: x is an apartment

Hx: x is a house

Lx: x is large

Bxy: x is bigger than y

(∃x)[(Ax • Lx) • (∃y)(Hy • Bxy)]

Some large houses are bigger than some apartments.

Some houses are bigger than all large apartments.

Some large apartments are bigger than some houses.

Some houses are bigger thatn some large apartments.

Some large apartments are bigger than all houses.

.

Select the best English interpretation of the given proposition, using the following translation key:

Ax: x is an apartment

Hx: x is a house

Lx: x is large

Bxy: x is bigger than y

(∀x){Ax ⊃ (∀y)[(Hy • Ly) ⊃ ∼Bxy]}

All apartments are not bigger than some large house.

No apartment is bigger than any large house.

All large houses are not bigger than some apartment.

No large house is bigger than all apartments.

No apartment is bigger than no large house.

.

Select the best English interpretation of the given proposition, using the following translation key:

Ax: x is an apartment

Hx: x is a house

Lx: x is large

Bxy: x is bigger than y

(∀x){(Lx • Ax) ⊃ (∃y)[(Hy • ~Ly) • Bxy]}

All large apartments are bigger than all houses that are not large.

Some house that is not large is bigger than all large apartments.

Any apartment bigger than a house that is not large is large.

Any large apartment is bigger than an apartment that is not large.

Every large apartment is bigger than some house that is not large.

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