Deck 4: Monadic Predicate Logic

Question 1

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Abhishek loves ice cream and pizza.

A) Ai • ∼Ap
B) aI • aP
C) Ai ⊃ Ap
D) Ia • Pa
E) Ia ⊃ Pa

Answer 1

D

Question 2

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Bonita doesn't study law; she's pre-med.

A) ∼Lb • Mb
B) ∼Lb ⊃ Mb
C) ∼Bl $\lor$ Bm
D) ∼Bl ⊃ Bm
E) Lb • Mb

Answer 2

A

Question 3

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-If Carla works for an airline, then Darlene doesn't.

A) Ad $\lor$ ∼Ac
B) Ax ⊃ ∼Ay
C) Ac ≡ ∼Ad
D) Ac • ∼Ad
E) Ac ⊃ ∼Ad

Answer 3

E

Question 4

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Efraim takes acting classes if, and only if, he gets time off from work.

A) Ex ≡ Wy
B) Ae ⊃ We
C) ∼Ae $\lor$ We
D) We ⊃ Ae
E) Ae ≡ We

Question 5

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Farzona's dropping art history is a sufficient condition for her being unhappy.

A) Uf ≡ Af
B) Af ⊃ Uf
C) Fa ≡ Uf
D) Af • Fu
E) Fa ≡ Fu

Question 6

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Neither Gabriel nor Honoré play volleyball.

A) ∼(∼Vg • ∼Vh)
B) ∼Vg $\lor$ ∼Vh
C) ∼(Vg • Vh)
D) ∼(Vg $\lor$ Vh)
E) ∼(Vg • ∼Vh)

Question 7

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Izzy takes linear algebra only if she does not take discrete mathematics.

A) ∼Li ⊃ Di
B) Di ≡ ∼Li
C) Li ⊃ ∼Di
D) Li ≡ Di
E) ∼Di ⊃ ∼Li

Question 8

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Kyrone has a thriving practice if Jalissa stops touring.

A) Tj ⊃ Pk
B) Tj $\lor$ Pk
C) Tj ⊃ ∼Pk
D) ∼Kp ⊃ Jt
E) Jt ≡ Kp

Question 9

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Whatever Lola wants, Lola gets.

A) (∀x)(Gx ≡ Wx)
B) (∀x)(Wx $\lor$ Gx)
C) (∀x)(Wx ⊃ Gx)
D) (∃x)(Wx $\lor$ Gx)
E) (∃x)(Wx ⊃ Gx)

Question 10

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-If Tranh takes a sabbatical then neither she nor Minh will feel overworked.

A) St ⊃ (∼Ot $\lor$ Om)
B) St ⊃ ∼(Ot $\lor$ Om)
C) St ⊃ ∼(Ot $\lor$ ∼Om)
D) St ⊃ (Ot $\lor$ Om)
E) St ⊃ ∼(∼Ot $\lor$ Om)

Question 11

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-All mammals feed their young.

A) Mf
B) (∃x)(Mx ⊃ Fx)
C) Fm
D) (∀x)(Mx ≡ Fx)
E) (∀x)(Mx ⊃ Fx)

Question 12

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Some cherries are red.

A) Sc • Rc
B) (∃x)(Cx ⊃ Rx)
C) Cs • Cr
D) (∃x)(Cx • Rx)
E) (∀x)(Cx • Rx)

Question 13

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Some blankets are not soft.

A) (∃x)(Bx • ∼Sx)
B) ∼ (∃x)(Bx • Sx)
C) ∼ (∃x)(Bx • ∼Sx)
D) ∼ (∃x)( ∼Bx • ∼Sx)
E) ∼ (∃x)(Bx ⊃ ∼Sx)

Question 14

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Some grass is high and thick.

A) (∃x)[Gx $\lor$ (Hx • Tx)]
B) (∃x)[Gx $\lor$ (Hx $\lor$ Tx)]
C) (∃x)[Gx • (Hx • Tx)]
D) (∃x)[Gx ⊃ (Hx $\lor$ Tx)]
E) (∃x)[Gx • (Hx $\lor$ Tx)]

Question 15

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-No humans don't have a mother.

A) (∀x)(Hx ⊃ ∼∼Mx)
B) (∃x)(Hx ⊃ ∼Mx)
C) ∼(∀x)(Hx ⊃ Mx)
D) (∀x)(Hx ⊃ ∼Mx)
E) (∃x)(Hx • ∼Mx)

Question 16

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Some visitors did not stay for dinner.

A) (∀x)(∼Vx • Sx)
B) (∃x)(∼Vx • ∼Sx)
C) (∃x)(Vx ⊃ ∼Sx)
D) (∃x)(Vx • ∼Sx)
E) (∀x)(Vx • ∼Sx)

Question 17

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-No visitor stayed for dinner.

A) ∼(∀x)(Vx ⊃ Sx)
B) ∼(∀x)(Vx ⊃ ∼Sx)
C) (∀x) (Vx ⊃ Sx)
D) (∀x)∼(Vx ⊃ ∼Sx)
E) (∀x)(Vx ⊃ ∼Sx)

Question 18

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Some educated doctors are not gentle.

A) (∃x) (Dx • Ex)
B) (∃x)[(Dx • Ex) • ∼Gx]
C) (∃x)[(Dx • Ex) ⊃ ∼Gx]
D) (∃x)[(Dx • Ex) • Gx]
E) (∃x) ∼[(Dx • Ex) ⊃ ∼Gx]

Question 19

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-No red flowers are in the garden.

A) ∼(∀x)[(Rx • Fx) ⊃ Gx]
B) (∀x)[(Rx • Fx) ⊃ ∼Gx]
C) (∀x)∼[(Rx • Fx) ⊃ Gx]
D) (∃x)[(Rx • Fx) ⊃ ∼Gx]
E) (∃x)[(Rx • Fx) • ∼Gx]

Question 20

For each of the following sentences, select the best translation into predicate logic, using the given constants and predicates.
-Some yellow birds both chirp and sing.

A) (∃x)[(Yx • Bx) • (Cx • Sx)]
B) (∃x)(Yx • Bx) • Sx
C) (∃x)(Sx • Bx) • Yx
D) (∃x)[(Yx • Bx) ⊃ (Cx • Sx)]
E) (∃x)[(Yx • Bx) ⊃ (Cx ⊃ Sx)]

Question 21

select the best translation into predicate logic.
-All tall athletes work hard.

A) (∀x)[Wx ⊃ (Tx • Ax)]
B) (∀x)[(Tx $\lor$ Ax) ⊃ Wx]
C) (∀x)[Wx ⊃ (Tx $\lor$ Ax)]
D) (∀x)[(Tx • Ax) ⊃ Wx]

Question 22

select the best translation into predicate logic.
-Some tall athletes don't receive scholarships.

A) (∀x)[(Ax • Tx) ⊃ ∼Sx]
B) (∃x)[(Ax • Tx) • ∼Sx]
C) (∃x)[(Ax $\lor$ Tx) • ∼Sx]
D) (∃x)[(Ax • Tx) ⊃ ∼Sx]

Question 23

select the best translation into predicate logic.
-Only tall athletes play professional basketball.

A) (∀x)[Px ⊃ (Tx • Ax)]
B) (∀x)[(Tx • Ax) ⊃ Px]
C) (∀x)[(Tx $\lor$ Ax) ⊃ Px]
D) (∀x)[Px ≡ (Tx • Ax)]

Question 24

select the best translation into predicate logic.
-Tall athletes with determination either receive scholarships or play professional sports.

A) (∃x){[(Tx • Ax) • Dx] ⊃ (Sx $\lor$ Px)}
B) (∀x){(Sx $\lor$ Px) ⊃ [(Tx • Ax) • Dx]}
C) (∀x){[(Tx • Ax) • Dx] ⊃ (Sx $\lor$ Px)}
D) (∃x){[(Tx • Ax) • Dx] ≡ (Sx $\lor$ Px)}

Question 25

select the best translation into predicate logic.
-Some athletes who don't work hard receive scholarships, if, and only if, no athletes who play professional sports don't have determination.

A) (∃x)[(Ax • ∼Wx) • Sx] ≡ (∀x)[(Ax • Px) ⊃ ∼∼Dx]
B) (∃x)[(Ax • ∼Wx) • Sx] ⊃ (∀x)[(Ax • Px) ⊃ ∼∼Dx]
C) (∃x)[(Ax • ∼Wx) • Sx] ⊃ (∀x)[(Ax • Px) ⊃ ∼Dx]
D) (∃x)[(Ax • ∼Wx) • Sx] ≡ (∀x)[(Ax • Px) ⊃ ∼Dx]

Question 26

select the best translation into predicate logic.
-Some athletes play professional sports if, and only if, they have determination.

A) (∃x)[(Ax • Px) ⊃ Dx)]
B) (∃x)[Dx ⊃ (Ax • Px)]
C) (∃x)[Ax ⊃ (Px ≡ Dx)]
D) (∃x)[Ax • (Px ≡ Dx)]

Question 27

select the best translation into predicate logic.
-Only athletes who are tall and work hard play professional sports.

A) (∀x){[Ax • (Tx • Wx)] ⊃ Px}
B) (∀x)[(Px • Ax) ⊃ (Tx $\lor$ Wx)]
C) (∀x){Px ⊃ [Ax • (Tx • Wx)]}
D) (∀x){[Ax • (Tx $\lor$ Wx)] ⊃ Px}

Question 28

select the best translation into predicate logic.
-No athletes who play professional sports and have determination are neither tall nor work hard.

A) (∀x){[(Ax • Px) • Dx] ⊃ ∼(Tx $\lor$ Wx)}
B) (∀x){[(Ax • Px) • Dx] ⊃ ∼∼(Tx $\lor$ Wx)}
C) (∀x){[(Ax • Px) • Dx] ⊃ (∼Tx $\lor$ ∼Wx)}
D) ∼ (∀x){[(Ax • Px) • Dx] ⊃ (Tx $\lor$ Wx)}

Question 29

select the best translation into predicate logic.
-Some rationalists who are skeptics are not theists.

A) (∃x)[(Rx • Sx) • ∼Tx]
B) ∼(∃x)[(Rx • Sx) • Tx]
C) (∃x)[(Rx • Sx) ⊃ ∼Tx]
D) (∃x)[(Rx • Sx) $\lor$ ∼Tx]

Question 30

select the best translation into predicate logic.
-All idealists are apriorists, but not theists.

A) (∀x)[(Ix ⊃ Ax) • ∼Tx]
B) (∀x)[Ix ⊃ (∼Ax • Tx)]
C) (∀x)(Ix ⊃ Ax} $\lor$ (∀x)(Tx ⊃ ∼Ax)
D) (∀x)[Ix ⊃ (Ax • ∼Tx)]

Question 31

select the best translation into predicate logic.
-Berkeley is an empiricist and Hume is not an apriorist.

A) Eb • Ah
B) ∼Eb • ∼Ah
C) Eb • ∼Ah
D) (∃x)(Ex • ∼Ax)

Question 32

select the best translation into predicate logic.
-If some idealists are not skeptics then not all theists are rationalists.

A) (∃x)(Ix • ∼Sx) ⊃ ∼(∀x)(Tx ⊃ Rx)
B) (∃x)(Ix • ∼Sx) ⊃ (∀x)(Tx ⊃ ∼Rx)
C) (∃x)(Ix • ∼Sx) ⊃ ∼(∀x) ∼(Tx ⊃ Rx)
D) (∃x)(Ix • ∼Sx) ⊃ ∼(∃x)(Tx • Rx)

Question 33

select the best translation into predicate logic.
-No apriorist rationalists are skeptics, but Hume is.

A) (∀x)[(Ax • Rx) ⊃ Sx] • Sh
B) (∀x)[(Ax • Rx) ⊃ ∼Sx] • Sh
C) ∼(∀x)[(Ax • Rx) ⊃ Sx] • Sh
D) ∼(∀x)[(Ax • Rx) ⊃ ∼Sx] • Sh

Question 34

select the best translation into predicate logic.
-Only consistent rationalists are apriorists.

A) (∀x)[(Cx • Rx)] ⊃ Ax]
B) (∀x)[Ax ≡ (Cx • Rx)]
C) (∀x)[(Rx $\lor$ Ax) ⊃ Cx]
D) (∀x)[(Rx • Ax) ⊃ Cx]

Question 35

select the best translation into predicate logic.
-Everyone is a theist unless someone is a skeptic and not an apriorist.

A) (∀x)(Px ⊃ Tx) ⊃ (∃x)(Sx • ∼Ax)
B) (∀x)(Px ⊃ Tx) $\lor$ (∃x)(Sx $\lor$ ∼Ax)
C) (∀x)(Px ⊃ Tx) ⊃ (∃x)(Sx $\lor$ ∼Ax)
D) (∀x)(Px ⊃ Tx) $\lor$ (∃x)(Sx • ∼Ax)

Question 36

select the best translation into predicate logic.
-Some apriorist is a skeptic if, and only if, s/he is an inconsistent empiricist.

A) (∃x)[(Ax • Sx) ⊃ (Ex • ∼Cx)]
B) (∃x)[(Ax • Sx) ≡ (Ex $\lor$ ∼Cx)]
C) (∃x)[(Ax • Sx) ≡ (Ex • ∼Cx)]
D) (∃x)[(Ax • Sx) ⊃ (Ex $\lor$ ∼Cx)]

Question 37

select the best translation into predicate logic.
-Some settlements are not on the water.

A) ∼(∃x)(Sx • ∼Wx)
B) ∼(∃x)(Sx • Wx)
C) (∃x)(Sx • ∼Wx)
D) (∃x)(Sx $\lor$ ∼Wx)

Question 38

select the best translation into predicate logic.
-There are no settlements on the water with trading ports.

A) (∀x)[(Sx • Wx) ⊃ ∼Tx]
B) ∼(∀x)[(Sx • Wx) ⊃ Tx]
C) (∀x)[(Sx ⊃ ∼(Wx $\lor$ Tx)]
D) (∀x)[(Sx ⊃ (∼Wx • ∼Tx)]

Question 39

select the best translation into predicate logic.
-Not all the settlements have trading ports.

A) (∀x)(Sx ⊃ ∼Tx)
B) ∼(∀x)(Sx ⊃ Tx)
C) ∼(∀x)(Sx ⊃ ∼Tx)
D) (∀x)(Sx ⊃ Tx)

Question 40

select the best translation into predicate logic.
-Either Tortuga is a city or it is not a settlement.

A) Ct $\lor$ ∼St
B) tC $\lor$ ∼tS
C) (∃x)(Cx $\lor$ ∼Sx)
D) (∃x)(Cx • ∼Sx)

Question 41

select the best translation into predicate logic.
-All cities and settlements are nicely placed and productive.

A) (∀x)[(Cx • Sx) ⊃ (Nx • Px)]
B) (∀x)[(Cx • Sx) • (Nx • Px)]
C) (∀x)[(Cx $\lor$ Sx) • (Nx • Px)]
D) (∀x)[(Cx $\lor$ Sx) ⊃ (Nx • Px)]

Question 42

select the best translation into predicate logic.
-If Tortuga is a city, then some settlements are not nicely placed.

A) Ct ⊃ ∼(∃x)(Sx • Nx)
B) Ct ⊃ (∃x)(Sx ⊃ ∼Nx)
C) Ct ⊃ (∃x)(Sx • ∼Nx)
D) (∃x)[Ct ⊃ (Sx • ∼Nx)]

Question 43

select the best translation into predicate logic.
-Either only cities are nicely placed or some settlements are not productive.

A) (∀x)(Cx ⊃ Nx) $\lor$ (∃x)(Sx • ∼Px)
B) (∀x)(Nx ⊃ Cx) $\lor$ (∃x)(Sx • ∼Px)
C) (∀x)(Cx ⊃ Nx) $\lor$ ∼(∃x)(Sx • Px)
D) (∀x)(Nx ⊃ Cx) $\lor$ ∼(∃x)(Sx • ∼Px)

Question 44

select the best translation into predicate logic.
-All cities are productive if and only if they are both nicely placed and not on the water.

A) (∀x){Cx ⊃ [Px ≡ (Nx • ∼Wx)]}
B) (∀x){Px ⊃ [Cx ≡ (Nx • ∼Wx)]}
C) (∀x){Px ⊃ [Cx ≡ ∼ (Nx • Wx)]}
D) (∀x){Cx ⊃ [Px ≡ ∼ (Nx • Wx)]}

Question 45

select the best English interpretation of the given statements of predicate logic.
f: Fifi
g: Gigi
Px: x is a poodle Qx: x is abused
Rx: x is loved
Sx: x will fetch balls
Tx: x will fetch sticks.
-(Pf • Pg) • [(Rf • Rg) • (Sf • ∼Sg)]

A) Fifi and Gigi are poodles, and both are loved, though Fifi will fetch balls while Gigi will not.
B) Fifi and Gigi are poodles, and both are loved, though neither will fetch balls.
C) Fifi is a poodle and Gigi is a poodle, and both are loved, or neither will fetch balls.
D) If Fifi and Gigi are poodles, then both are loved, though Fifi will fetch balls while Gigi will not.

Question 46

select the best English interpretation of the given statements of predicate logic.
f: Fifi
g: Gigi
Px: x is a poodle Qx: x is abused
Rx: x is loved
Sx: x will fetch balls
Tx: x will fetch sticks.
-(∀x)[(Px • Qx) ⊃ ∼Rx]

A) If poodles are loved, then they are not abused.
B) Only abused poodles are loved.
C) All abused poodles are loved.
D) No abused poodles are loved.

Question 47

select the best English interpretation of the given statements of predicate logic.
f: Fifi
g: Gigi
Px: x is a poodle Qx: x is abused
Rx: x is loved
Sx: x will fetch balls
Tx: x will fetch sticks.
-(∃x)[(Px • Rx) • (Sx • Tx)]

A) Only if poodles fetch balls and sticks are they loved.
B) If poodles are loved, they will fetch balls and sticks.
C) Some loved poodles will fetch balls and sticks.
D) Some loved poodles will fetch balls and sticks, but some will not.

Question 48

select the best English interpretation of the given statements of predicate logic.
f: Fifi
g: Gigi
Px: x is a poodle Qx: x is abused
Rx: x is loved
Sx: x will fetch balls
Tx: x will fetch sticks.
-(∀x)(Px ⊃ Qx) ⊃ (∃x)(Px • ∼Rx)

A) If all poodles are abused, then some poodles are loved.
B) If no poodles are loved, then some poodles are abused.
C) If all poodles are abused, then some poodles are not loved.
D) If some poodles are abused, then no poodles are loved.

Question 49

select the best English interpretation of the given statements of predicate logic.
f: Fifi
g: Gigi
Px: x is a poodle Qx: x is abused
Rx: x is loved
Sx: x will fetch balls
Tx: x will fetch sticks.
-(∀x){(Px • Qx) ⊃ [(Rx ⊃ (∼Sx ⊃ Tx)]}

A) All abused poodles are loved only if they will fetch sticks and will not fetch balls.
B) No abused poodles will fetch sticks if they will fetch balls, and if they are loved.
C) All abused poodles, if they are loved, will fetch sticks if they will not fetch balls.
D) All abused poodles are loved if they will fetch sticks or balls.
E) No abused poodles will not fetch balls, if they fetch sticks and are loved.

Question 50

select the best English interpretation of the given statements of predicate logic.
f: Fifi
g: Gigi
Px: x is a poodle Qx: x is abused
Rx: x is loved
Sx: x will fetch balls
Tx: x will fetch sticks.
-(∃x)[Px • (∼Qx • Rx)] ⊃ (∀x)[(Px • Rx) ⊃ Tx)]

A) If some poodles are neither abused nor loved, then all loved poodles will fetch sticks.
B) If some poodles are not abused but are loved, then all loved poodles will fetch sticks.
C) Some poodles are neither abused nor loved, and all loved poodles will fetch sticks.
D) Some poodles are abused and unloved, but all loved poodles will fetch sticks.

Question 51

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $\lor$ Dx)]
-Which wffs below are not in the scope of '(∃x)'?

A) Ax
B) ∼(Cx $\lor$ Dx)
C) (Ax • ∼Bx) • ∼(Cx $\lor$ Dx)
D) All of the above.
E) None of the above.

Question 52

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $\lor$ Dx)]
-Which variables are bound by the '(∃x)'?

A) The x that follows the A.
B) The x that follows the B.
C) The x that follows the C.
D) The x that follows the D.
E) All of the above.

Question 53

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $\lor$ Dx)]
-Is the formula open or closed?

A) Open
B) Closed

Question 54

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $\lor$ Dx)]
-Which of the following variables in the formula are free?

A) The x that follows the A.
B) The x that follows the B.
C) The x that follows the C.
D) All of the above.
E) None of the above.

Question 55

refer to the following formula: (∃x)[(Ax • ∼Bx) • ∼(Cx $\lor$ Dx)]
-Which is the main operator of the formula?

A) ∃x
B) $\lor$
C) ∼
D) •
E) None of the above.

Question 56

refer to the following formula: (∀x)[(Ex $\lor$ Fx) ⊃ (Gx • Hd)]
-Which wffs below are not in the scope of '(∀x)'?

A) Ex
B) Hd
C) Ex $\lor$ Fx
D) All of the above.
E) None of the above.

Question 57

refer to the following formula: (∀x)[(Ex $\lor$ Fx) ⊃ (Gx • Hd)]
-Which variables are bound by the '(∀x)'?

A) The x that follows the E.
B) The x that follows the F.
C) The x that follows the G.
D) All of the above.
E) None of the above.

Question 58

refer to the following formula: (∀x)[(Ex $\lor$ Fx) ⊃ (Gx • Hd)]
-Is the formula open or closed?

A) Open
B) Closed

Question 59

refer to the following formula: (∀x)[(Ex $\lor$ Fx) ⊃ (Gx • Hd)]
-Which of the following variables in the formula are free?

A) The x that follows the E.
B) The x that follows the F.
C) The x that follows the G.
D) All of the above.
E) None of the above.

Question 60

refer to the following formula: (∀x)[(Ex $\lor$ Fx) ⊃ (Gx • Hd)]
-Which is the main operator of the formula?

A) ∀x
B) $\lor$
C) ⊃
D) •
E) None of the above.

Question 61

refer to the following formula:
∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]}
-Which wffs below are not in the scope of '(∀x)'?

A) Lb
B) La
C) La • Lb
D) Kx ≡ (La • Lb)
E) None of the above.

Question 62

refer to the following formula:
∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]}
-Which variables are bound by the '(∀x)'?

A) The x that follows the I.
B) The x that follows the J.
C) The x that follows the K.
D) All of the above.
E) None of the above.

Question 63

refer to the following formula:
∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]}
-Is the formula open or closed?

A) Open
B) Closed

Question 64

refer to the following formula:
∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]}
-Which of the following variables in the formula are free?

A) The x that follows the I.
B) The x that follows the J.
C) The x that follows the K.
D) All of the above.
E) None of the above.

Question 65

refer to the following formula:
∼(∀x){(Ix • Jx) ⊃ [Kx ≡ (La • Lb)]}
-Which is the main operator of the formula?

A) ∀x
B) ≡
C) ⊃
D) •
E) ∼

Question 66

refer to the following formula: (∃x)[Mx • (∼Nc $\lor$ ∼Ox)] ≡ (Py • Pb)
-Which wffs below are not in the scope of '(∃x)'?

A) ∼(Py • Pb)
B) Mx
C) Nc
D) Mx • (∼Nc $\lor$ ∼Ox)
E) None of the above.

Question 67

refer to the following formula: (∃x)[Mx • (∼Nc $\lor$ ∼Ox)] ≡ (Py • Pb)
-Which variables are bound by the '(∃x)'?

A) The x that follows the M.
B) The x that follows the O.
C) The y that follows the P.
D) None of the above.
E) Both A and B.

Question 68

refer to the following formula: (∃x)[Mx • (∼Nc $\lor$ ∼Ox)] ≡ (Py • Pb)
-Is the formula open or closed?

A) Open
B) Closed

Question 69

refer to the following formula: (∃x)[Mx • (∼Nc $\lor$ ∼Ox)] ≡ (Py • Pb)
-Which of the following variables in the formula are free?

A) The x that follows the M.
B) The y that follows the P.
C) The x that follows the O.
D) All of the above.
E) None of the above.

Question 70

refer to the following formula: (∃x)[Mx • (∼Nc $\lor$ ∼Ox)] ≡ (Py • Pb)
-Which is the main operator of the formula?

A) (∃x)
B) The first '•', reading left to right.
C) ≡
D) $\lor$
E) There is no main operator.

Question 71

1. (∀x)(Cx ⊃ Dx)
2. (∀x)(Ex ⊃ ∼Dx)
-Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

A) Ca ⊃ Db
B) Ex ⊃ ∼Dc
C) Ex
D) Es ⊃ ∼Ds
E) Cx ⊃ Ds

Question 72

1. (∀x)(Cx ⊃ Dx)
2. (∀x)(Ex ⊃ ∼Dx)
-Which of the following propositions is derivable from the given premises in M?

A) (∀x)(Ex ⊃ Cx)
B) (∀x)(Ex ⊃ ∼Cx)
C) (∃x)Ex
D) (∃x)Dx
E) (∀x)(∼Ex $\lor$ Cx)

Question 73

1. (∀x)(Fx ⊃ ∼Gx)
2. (∃x)(Hx • Gx)
-Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

A) Hx • Gx
B) Hn • Gn
C) Fn ⊃ ∼Gx
D) Fx ⊃ ∼Gn
E) Hn

Question 74

1. (∀x)(Fx ⊃ ∼Gx)
2. (∃x)(Hx • Gx)
-Which of the following propositions is derivable from the given premises in M?

A) (∀x)(Hx • ∼Fx)
B) (∃x)(∼Hx • ∼Fx)
C) (∀x)(Hx • Fx)
D) (∃x)(Hx • Fx)
E) (∃x)(Hx • ∼Fx)

Question 75

1. (∃x)(Kx $\lor$ Lx)
2. (∀x)(Jx ⊃ ~Lx)
-Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

A) Js ⊃ ~Ls
B) Kx $\lor$ Lx
C) Js ⊃ ~Lx
D) Kx $\lor$ Ly
E) Kn $\lor$ Lm

Question 76

1. (∃x)(Kx $\lor$ Lx)
2. (∀x)(Jx ⊃ ~Lx)
-Which of the following propositions is derivable from the given premises in M?

A) (∀x)(Kx $\lor$ Lx)
B) (∀x)(~Jx $\lor$ Kx)
C) (∃x)(~Jx $\lor$ Kx)
D) (∃x)~Jx
E) (∃x)Kx

Question 77

1. (∀x)(Hx ⊃ ∼Jx)
2. (∀x)(Ix ⊃ Jx)
3. Ha • Ib
-Which of the following propositions is an immediate (one-step) consequence in M of the given premises?

A) Hx • Ix
B) In ⊃ Jx
C) Hx ⊃ ∼Jx
D) Hx ⊃ ∼Js
E) Hx

Question 78

1. (∀x)(Hx ⊃ ∼Jx)
2. (∀x)(Ix ⊃ Jx)
3. Ha • Ib
-Which of the following propositions is derivable from the given premises in M?

A) (∀x)∼Jx
B) (∀x)Jx
C) ∼(Ix • Hx)
D) ∼(Ix $\lor$ Hx)
E) ∼(Ia $\lor$ Hb)

Question 79

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

A) Ax
B) Bx ⊃ Dx
C) Ba ⊃ Da
D) Ax ⊃ Bx
E) Ba

Question 80

1. (∀x)(Ax ⊃ Bx)
2. (∃x)Ax
3. (∃x)Bx ⊃ (∃x)Dx
-Which of the following propositions is derivable from the given premises in M?

A) (∃x)Dx
B) (∀x)Bx
C) (∃x)(Dx • Bx)
D) (∀x)(Dx • Bx)
E) (∀x)Ax