Section 4.02 Self Quiz

. Select the best translation into predicate logic: Some chairs are sturdy. No folding chairs are sturdy. Thus, some chairs don't fold.

1. (∃x)(Cx ⊃ Sx)
2. ~(∀x)(Fx ⊃ Sx) / (∃x)(Cx ⊃ ~Fx)

1. (∃x)(Cx ⊃ Sx)
2. ~(∀x)(Fx ⊃ Sx) / (∃x)(Cx • ~Fx)

1. (∃x)(Cx • Sx)
2. ~(∀x)(Fx ⊃ Sx) / (∃x)(Cx • ~Fx)

1. (∃x)(Cx • Sx)
2. (∀x)(Fx ⊃ ~Sx) / (∃x)(Cx • ~Fx)

. Select the best translation into predicate logic: All schools are either public or private. Some schools aren't private. So something is public.

1. (∀x)[Sx ⊃ (Lx ∨ Px)]
2. (∃x)(Sx • ~Px) / (∃x)Lx

1. (∀x)[Sx ⊃ (Lx • Px)]
2. (∃x)(Sx • ~Px) / Ps

1. (∀x)[Sx ⊃ (Lx ∨ Px)]
2. (∃x)(Sx • ~Px) / (∀x)Lx

1. (∀x)[Sx ⊃ (Lx ∨ Px)]
2. (∃x)(Sx ∨ ~Px) / (∃x)Lx

. Select the best translation into predicate logic: Judges and lawyers are politicians. No Floridian is biased. Some judges are Floridians. So some politicians are unbiased.

1. (∀x)[(Jx • Lx) ⊃ Px]
2. ~ (∀x)(Fx ⊃ Bx)
3. (∃x)(Jx • Fx) / (∃x)(Px • ~Bx)

1. (∀x)[(Jx ∨ Lx) ⊃ Px]
2. (∀x)(Fx ⊃ ~Bx)
3. (∃x)(Jx • Fx) / (∃x)(Px • ~Bx)

1. (∀x)[(Jx • Lx) ⊃ Px]
2. (∀x)(Fx ⊃ ~Bx)
3. (∃x)(Jx • Fx) / (∃x)(Px • ~Bx)

1. (∀x)[(Jx ∨ Lx) ⊃ Px]
2. ~ (∀x)(Fx ⊃ Bx)
3. (∃x)(Jx • Fx) / (∃x)(Px • ~Bx)

. Select the best translation into predicate logic: Some apples are aren't green. All apples are fruit. So, some apples are fruit that's not green.

1. (∃x)(Ax • ~Gx)
2. (∀x)(Ax ⊃ Fx) / (∃x)Ax • (∃x)(Fx • ~Gx)

1. (∃x)(Ax • ~Gx)
2. (∀x)(Ax ⊃ Fx) / ~ (∃x)[(Ax • (Fx • Gx)]

1. (∃x)(Ax • ~Gx)
2. (∀x)(Ax ⊃ Fx) / (∃x)[(Ax • (Fx • ~Gx)]

1. (∃x)(Ax ⊃ ~Gx)
2. (∀x)(Ax ⊃ Fx) / ~ (∃x)[(Ax • (Fx • Gx)]

. Select the best translation into predicate logic: If all Martians are wonderful, then some Venutians are also. But there are no Venutians. So, something isn't wonderful.

1. (∀x)(Mx ⊃ Wx) ⊃ (∃x)(Vx • Wx)
2. ~(∃x)Vx / (∃x)~Wx

1. (∀x)(Mx ⊃ Wx) ⊃ (∃x)(Vx • Wx)
2. ~(∃x)Vx / ~(∃x)Wx

1. (∀x)(Mx ⊃ Wx) ⊃ (∃x)(Vx • Wx)
2. (∃x)~Vx / (∃x)~Wx

1. (∀x)(Mx ⊃ Wx) ⊃ (∃x)(Vx • Wx)
2. (∃x)~Vx / ~(∃x)Wx

. Select the best translation into predicate logic: If all books are wonderful, then some movies are, too. But there are no movies. So, something isn't wonderful.

1. (∀x)(Bx ⊃ Wx) ⊃ (∃x)(Mx • Wx)
2. ~(∃x)Mx / ~(∃x) Wx

1. (∀x)(Bx ⊃ Wx) ⊃ (∃x)(Mx • Wx)
2. (∃x)~Mx / (∃x)~Wx

1. (∀x)(Bx ⊃ Wx) ⊃ (∃x)(Mx • Wx)
2. (∃x)~Mx / ~(∃x)Wx

1. (∀x)(Bx ⊃ Wx) ⊃ (∃x)(Mx • Wx)
2. ~(∃x)Mx / (∃x)~Wx

. Select the best translation into predicate logic: All philosophers are scrawny. Jared is not scrawny. Therefore, Jared is not a philosopher.

1. (∀x)(Px • Sx)
2. ~Sj / ~Pj

1. (∀x)(Px ⊃ Sx)
2. ~Sj / ~Pj

1. (∀x)(Px ≡ Sx)
2. ~Sj / ~Pj

1. (∀x)(Px ⊃ Sx)
2. ~sJ / ~pJ

. Select the best translation into predicate logic: Tigers are fierce and dangerous. Some tigers are beautiful. Therefore, some dangerous things are beautiful.

1. (∀x)[Tx ⊃ (Fx ∨ Dx)]
2. (∃x)(Tx • Bx) / (∃x)(Dx • Bx)

1. (∀x)[Tx ⊃ (Fx • Dx)]
2. (∃x)(Tx • Bx) / (∃x)(Dx • Bx)

1. (∀x)[Tx ⊃ (Fx • Dx)]
2. (∀x)(Tx ⊃ Bx) / (∀x)(Dx ⊃ Bx)

1. (∀x)[Tx ⊃ (Fx ∨ Dx)]
2. (∀x)(Tx ⊃ Bx) / (∀x)(Dx ⊃ Bx)

. Select the best translation into predicate logic: All liars are mendacious. Some liars are journalists. Therefore, some journalists are mendacious.

1. (∀x)(Lx ⊃ Mx)
2. (∃x)(Lx ⊃ Jx) / (∃x)(Jx ⊃ Mx)

1. (∃x)(Lx ⊃ Mx)
2. (∃x)(Lx • Jx) / (∃x)(Jx • Mx)

1. (∀x)(Lx ⊃ Mx)
2. (∃x)(Lx • Jx) / (∃x)(Jx • Mx)

1. (∀x)(Lx ≡ Mx)
2. (∃x)(Lx • Jx) / (∃x)(Jx ⊃ Mx)

. Select the best translation into predicate logic: If some flight attendants are underpaid, then all technicians are, too. But it is not the case that all flight attendants are not underpaid. So, it's false that some technicians are not underpaid.

1. (∃x)(Fx • Ux) ⊃ (∀x)(Tx ⊃ Ux)
2. ~(∀x)(Fx ⊃ ~Ux) / ~(∃x)(Tx • ~Ux)

1. (∃x)[(Fx • Ux) ⊃ (Tx ⊃ Ux)]
2. ~(∀x)(Fx ⊃ ~Ux) / ~(∃x)(Tx • ~Ux)

1. (∃x)(Fx • Ux) ⊃ (∀x)(Tx ⊃ Ux)
2. (∀x)(Fx ⊃ ~Ux) / ~(∃x)~(Tx • Ux)

1. (∃x)(Fx • Ux) ⊃ (∀x)(Tx ⊃ Ux)
2. (∀x)(Fx ⊃ ~Ux) / ~(∃x)(Tx • ~Ux)

. Select the best translation into predicate logic: Either some acts are immoral, or no acts are forbidden. But some acts are forbidden. So, it's false that all acts are moral.

1. (∃x)(Ax • ~Mx) ∨ (∀x)(Ax ⊃ ~Fx)
2. (∃x)(Ax • Fx) / (∀x)(Ax ⊃ ~Mx)

1. (∃x)(Ax • ~Mx) ∨ ~(∀x)(Ax ⊃ Fx)
2. (∃x)(Ax • Fx) / ~(∀x)(Ax ⊃ Mx)

1. (∃x)(Ax • ~Mx) ∨ ~(∀x)(Ax ⊃ Fx)
2. (∃x)(Ax • Fx) / (∀x)(Ax ⊃ ~Mx)

1. (∃x)(Ax • ~Mx) ∨ (∀x)(Ax ⊃ ~Fx)
2. (∃x)(Ax • Fx) / ~(∀x)(Ax ⊃ Mx)

. Select the best translation into predicate logic: If all social workers are underpaid, then some teachers are, too. It's false that teachers exist. So, something isn't underpaid.

1. (∀x)(Sx ⊃ Ux) ⊃ (∃x)(Tx • Ux)
2. (∃x)~Tx / (∃x)~Ux

1. (∀x)(Sx ⊃ Ux) ⊃ (∃x)(Tx • Ux)
2. ~(∃x)Tx / ~(∃x) Ux

1. (∀x)(Sx ⊃ Ux) ⊃ (∃x)(Tx • Ux)
2. ~(∃x)Tx / (∃x)~Ux

1. (∀x)(Sx ⊃ Ux) ⊃ (∃x)(Tx • Ux)
2. ~(∃x)~Tx / ~(∃x)Ux

. Select the best translation into predicate logic: Teachers and social workers are college graduates. Any altruist is an idealist. Some social workers are not idealists. Some teachers are altruists. Therefore, some college graduates are idealists.

1. (∀x)[(Tx • Sx) ⊃ Cx]
2. (∀x)(Ax ⊃ Ix)
3. (∃x)(Sx • ~Ix)
4. (∃x)(Tx • Ax) / (∃x)(Cx • Ix)

1. [(∀x)(Tx ∨ Sx) ⊃ Cx]
2. (∀x)(Ax ⊃ Ix)
3. (∃x)(Sx • ~Ix)
4. (∃x)(Tx • Ax) / (∃x)(Cx • Ix)

1. [(∀x)(Tx • Sx) ⊃ Cx]
2. (∃x)(Ax • Ix)
3. (∃x)(Sx • ~Ix)
4. (∃x)(Tx • Ax) / (∃x)(Cx • Ix)

1. (∀x)[Cx ⊃ (Tx • Sx)]
2. (∀x)(Ax ⊃ Ix)
3. (∃x)(Sx • ~Ix)
4. (∃x)(Tx • Ax) / (∃x)(Cx • Ix)

. Select the best translation into predicate logic: All the accused are guilty. All who are convicted will hang. All who are guilty are convicted. So, all the accused will hang.

1. (∀x)(Ax ⊃ Gx)
2. (∀x)(Cx ⊃ Hx)
3. (∀x)(Gx ⊃ Cx) / (∀x)(Ax ⊃ Hx)

1. (∀x)(Ax • Gx)
2. (∀x)(Cx • Hx)
3. (∀x)(Gx • Cx) / (∀x)(Ax • Hx)

1. (∀x)(Ax ≡ Gx)
2. (∀x)(Cx ≡ Hx)
3. (∀x)(Gx ≡ Cx) / (∀x)(Ax ≡ Hx)

1. (∀x)(Ax ∨ Gx)
2. (∀x)(Cx ∨ Hx)
3. (∀x)(Gx ∨ Cx) / (∀x)(Ax ∨ Hx)

. Select the best translation into predicate logic: Boxers and wrestlers are athletes. Any athlete is hard-working. There are wrestlers who aren't strong. Therefore, not every hard-working thing is strong.

1. (∀x)[(Bx ∨ Wx) ⊃ Ax]
2. (∀x)(Ax ⊃ Hx)
3. (∃x)(Wx • ~Sx) / ~(∀x)(Hx ⊃ Sx)

1. (∀x)[(Bx • Wx) ⊃ Ax]
2. (∀x)(Ax ⊃ Hx)
3. (∃x)(Wx • ~Sx) / ~(∀x)(Hx ⊃ Sx)

1. (∀x)[(Bx • Wx) ⊃ Ax]
2. (∀x)(Ax ⊃ Hx)
3. (∃x)(Wx • ~Sx) / (∀x)(Hx ⊃ ~ Sx)

1. (∀x)[(Bx • Wx) ⊃ Ax]
2. (∀x)(Ax ⊃ Hx)
3. (∀x)(Wx ⊃ ~Sx) / (∀x)(Hx ⊃ ~Sx)

. Select the best English interpretation of the given arguments in predicate logic.
1. (∀x)Ax ⊃ ~Ce
2. (∀x)(Bx ⊃ Cx) / ~(∀x)(Cx • Be)

No atoms are created. All planets are created. So it's not the case that all atoms are planets.

If everything is made of atoms, then Earth is created. All planets are created. So it's not the case that Earth is created, and earth is a planet.

No atoms are created. All planets are created. So it's not the case that Earth is created, and earth is a planet.

If everything is made of atoms, then Earth is not created. All planets are created. So it's not the case that everything is created and Earth is a planet.

. Select the best English interpretation of the given arguments in predicate logic.
1. Dh ⊃ ~Pt
2. (∀x)Px ∨ (∀x)Mx
3. ~Mb / ~Dh

If my headache is dualist state, then your tickle is a physical state. Either everything is physical or everything is mental. But my broken toe is not a mental state. So my headache is not a dualist state.

If my headache is dualist state, then your tickle is not a physical state. Either everything is physical or everything is mental. But my broken toe is not a mental state. So my headache is not a dualist state.

If my headache is dualist state, then your tickle is not a physical state. If everything is physical then everything is mental. But my broken toe is not a mental state. So my headache is not a dualist state.

If my headache is dualist state, then your tickle is not a physical state. Everything is either physical or mental. But my broken toe is not a mental state. So my headache is not a dualist state.

. Select the best English interpretation of the given arguments in predicate logic.
1. Wn ∨ Wm
2. (∀x)[Lx ⊃ (Dx ⊃ ~Wx)]
3. Ln • Dn / ~(∀x)~Wx

Either Nancy or Marvin are at work. All lawyers are not at work if they are out to dinner. Nancy is a lawyer and out to dinner. So not everything is not at work.

Either Nancy or Marvin are at work. All lawyers are out to dinner if they are not at work. Nancy is a lawyer and out to dinner. So not everything is not at work.

Either Nancy or Marvin are at work. All lawyers are out to dinner if they are not at work. Nancy is a lawyer and out to dinner. So not everything is at work.

Either Nancy or Marvin are at work. All lawyers are not at work if they are out to dinner. Nancy is a lawyer and out to dinner. So not everything is at work.

. Select the best English interpretation of the given arguments in predicate logic.
1. (∃x)(Cx • Ox)
2. (∀x)[(~Cx ⊃ ~Bx) ⊃ ~Og] / ~Og

Some cookies have oatmeal. If something's not being a cookie entails that it doesn't have chocolate chips, then this cookie doesn't have oatmeal. So this cookie doesn't have oatmeal.

Some cookies have oatmeal. If something is not a cookie and does not have chocolate chips, it doesn't have oatmeal. So this cookie doesn't have oatmeal.

Some cookies have oatmeal. If something doesn't have oatmeal, then it is not a cookie and it doesn't have chocolate chips. So this cookie doesn't have oatmeal.

Some cookies have oatmeal. If something's not having chocolate chips entails that it is not a cookie, then it doesn't have oatmeal. So this cookie doesn't have oatmeal.

. Select the best English interpretation of the given arguments in predicate logic.
1. Dm
2. (∀x)(Wx ⊃ ~Dx)
3. (∀x)Wx ∨ Ag / (∃x)Ax

Marina is a dancer. Some weaklings are not dancers. Either everything is a weakling or Georgia plays volleyball. So something plays volleyball.

Marina is a dancer. No weakling is a dancer. Everything is either a weakling or plays volleyball. So something plays volleyball.

Marina is a dancer. Some weaklings are not dancers. Everything is either a weakling or plays volleyball. So something plays volleyball.

Marina is a dancer. No weakling is a dancer. Either everything is a weakling or Georgia plays volleyball. So something plays volleyball.

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