[["Question:  Which of the given formulas of PL is the best symbolization of the following sentence?\nEverybody loves Raymond, or not.\nChoices:\nA. L\nB. ~L\nC. L \u2022 ~L\nD. L \u2228 ~L\nAnswer:", " L"], ["Question:  Which of the given formulas of PL is the best symbolization of the following sentence?\nEverybody loves Raymond, or not.\nChoices:\nA. L\nB. ~L\nC. L \u2022 ~L\nD. L \u2228 ~L\nAnswer:", " ~L"], ["Question:  Which of the given formulas of PL is the best symbolization of the following sentence?\nEverybody loves Raymond, or not.\nChoices:\nA. L\nB. ~L\nC. L \u2022 ~L\nD. L \u2228 ~L\nAnswer:", " L \u2022 ~L"], ["Question:  Which of the given formulas of PL is the best symbolization of the following sentence?\nEverybody loves Raymond, or not.\nChoices:\nA. L\nB. ~L\nC. L \u2022 ~L\nD. L \u2228 ~L\nAnswer:", " L \u2228 ~L"], ["Question:  Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)\nQ \u2261 R\n~(S \u2228 Q) / R\nChoices:\nA. Valid\nB. Invalid. Counterexample when Q and S are true and R is false\nC. Invalid. Counterexample when Q is true and S and R are false\nD. Invalid. Counterexample when Q, S, and R are false\nAnswer:", " Valid"], ["Question:  Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)\nQ \u2261 R\n~(S \u2228 Q) / R\nChoices:\nA. Valid\nB. Invalid. Counterexample when Q and S are true and R is false\nC. Invalid. Counterexample when Q is true and S and R are false\nD. Invalid. Counterexample when Q, S, and R are false\nAnswer:", " Invalid. Counterexample when Q and S are true and R is false"], ["Question:  Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)\nQ \u2261 R\n~(S \u2228 Q) / R\nChoices:\nA. Valid\nB. Invalid. Counterexample when Q and S are true and R is false\nC. Invalid. Counterexample when Q is true and S and R are false\nD. Invalid. Counterexample when Q, S, and R are false\nAnswer:", " Invalid. Counterexample when Q is true and S and R are false"], ["Question:  Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)\nQ \u2261 R\n~(S \u2228 Q) / R\nChoices:\nA. Valid\nB. Invalid. Counterexample when Q and S are true and R is false\nC. Invalid. Counterexample when Q is true and S and R are false\nD. Invalid. Counterexample when Q, S, and R are false\nAnswer:", " Invalid. Counterexample when Q, S, and R are false"], ["Question:  Which of the given formulas of PL is the best symbolization of the following sentence?\nEither England's importing beef is a necessary condition for France's subsidizing agriculture or China's promoting human rights is not a sufficient condition for South Africa's supplying diamonds.\nChoices:\nA. (E \u2261 F) \u2228 ~(C \u2261 S)\nB. (E \u2261 F) \u2228 (~C \u2283 S)\nC. (E \u2283 F) \u2228 ~(C \u2283 S)\nD. (F \u2283 E) \u2228 ~(C \u2283 S)\nAnswer:", " (E \u2261 F) \u2228 ~(C \u2261 S)"], ["Question:  Which of the given formulas of PL is the best symbolization of the following sentence?\nEither England's importing beef is a necessary condition for France's subsidizing agriculture or China's promoting human rights is not a sufficient condition for South Africa's supplying diamonds.\nChoices:\nA. (E \u2261 F) \u2228 ~(C \u2261 S)\nB. (E \u2261 F) \u2228 (~C \u2283 S)\nC. (E \u2283 F) \u2228 ~(C \u2283 S)\nD. (F \u2283 E) \u2228 ~(C \u2283 S)\nAnswer:", " (E \u2261 F) \u2228 (~C \u2283 S)"], ["Question:  Which of the given formulas of PL is the best symbolization of the following sentence?\nEither England's importing beef is a necessary condition for France's subsidizing agriculture or China's promoting human rights is not a sufficient condition for South Africa's supplying diamonds.\nChoices:\nA. (E \u2261 F) \u2228 ~(C \u2261 S)\nB. (E \u2261 F) \u2228 (~C \u2283 S)\nC. (E \u2283 F) \u2228 ~(C \u2283 S)\nD. (F \u2283 E) \u2228 ~(C \u2283 S)\nAnswer:", " (E \u2283 F) \u2228 ~(C \u2283 S)"], ["Question:  Which of the given formulas of PL is the best symbolization of the following sentence?\nEither England's importing beef is a necessary condition for France's subsidizing agriculture or China's promoting human rights is not a sufficient condition for South Africa's supplying diamonds.\nChoices:\nA. (E \u2261 F) \u2228 ~(C \u2261 S)\nB. (E \u2261 F) \u2228 (~C \u2283 S)\nC. (E \u2283 F) \u2228 ~(C \u2283 S)\nD. (F \u2283 E) \u2228 ~(C \u2283 S)\nAnswer:", " (F \u2283 E) \u2228 ~(C \u2283 S)"], ["Question:  Select the best translation into predicate logic: Ms. Jackson lent me some sugar, but neither Janet nor Latoya did.\nChoices:\nA. Lm \u2228 ~(Jl \u2228 Ll)\nB. Lm \u2022 ~(Lj \u2022 Ll)\nC. Lm \u2022 ~(Lj \u2228 Ll)\nD. Lm \u2228 ~(Lj \u2022 Ll)\nAnswer:", " Lm \u2228 ~(Jl \u2228 Ll)"], ["Question:  Select the best translation into predicate logic: Ms. Jackson lent me some sugar, but neither Janet nor Latoya did.\nChoices:\nA. Lm \u2228 ~(Jl \u2228 Ll)\nB. Lm \u2022 ~(Lj \u2022 Ll)\nC. Lm \u2022 ~(Lj \u2228 Ll)\nD. Lm \u2228 ~(Lj \u2022 Ll)\nAnswer:", " Lm \u2022 ~(Lj \u2022 Ll)"], ["Question:  Select the best translation into predicate logic: Ms. Jackson lent me some sugar, but neither Janet nor Latoya did.\nChoices:\nA. Lm \u2228 ~(Jl \u2228 Ll)\nB. Lm \u2022 ~(Lj \u2022 Ll)\nC. Lm \u2022 ~(Lj \u2228 Ll)\nD. Lm \u2228 ~(Lj \u2022 Ll)\nAnswer:", " Lm \u2022 ~(Lj \u2228 Ll)"], ["Question:  Select the best translation into predicate logic: Ms. Jackson lent me some sugar, but neither Janet nor Latoya did.\nChoices:\nA. Lm \u2228 ~(Jl \u2228 Ll)\nB. Lm \u2022 ~(Lj \u2022 Ll)\nC. Lm \u2022 ~(Lj \u2228 Ll)\nD. Lm \u2228 ~(Lj \u2022 Ll)\nAnswer:", " Lm \u2228 ~(Lj \u2022 Ll)"], ["Question:  Select the best English interpretation of the given arguments in predicate logic.\nDh \u2283 ~Pt\n(\u2200x)Px \u2228 (\u2200x)Mx\n~Mb\t/ ~Dh\nChoices:\nA. 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.\nB. 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.\nC. 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.\nD. 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.\nAnswer:", " 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."], ["Question:  Select the best English interpretation of the given arguments in predicate logic.\nDh \u2283 ~Pt\n(\u2200x)Px \u2228 (\u2200x)Mx\n~Mb\t/ ~Dh\nChoices:\nA. 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.\nB. 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.\nC. 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.\nD. 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.\nAnswer:", " 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."], ["Question:  Select the best English interpretation of the given arguments in predicate logic.\nDh \u2283 ~Pt\n(\u2200x)Px \u2228 (\u2200x)Mx\n~Mb\t/ ~Dh\nChoices:\nA. 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.\nB. 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.\nC. 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.\nD. 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.\nAnswer:", " 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."], ["Question:  Select the best English interpretation of the given arguments in predicate logic.\nDh \u2283 ~Pt\n(\u2200x)Px \u2228 (\u2200x)Mx\n~Mb\t/ ~Dh\nChoices:\nA. 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.\nB. 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.\nC. 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.\nD. 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.\nAnswer:", " 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."], ["Question: Identify the antecedent of the following conditional proposition: The university raises tuition if, and only if, both the governor approves of it and the board of trustees recommends it.\nChoices:\nA. The university raises tuition.\nB. The governor approves of it.\nC. The board of trustees recommends it.\nD. None of the above\nAnswer:", " The university raises tuition."], ["Question: Identify the antecedent of the following conditional proposition: The university raises tuition if, and only if, both the governor approves of it and the board of trustees recommends it.\nChoices:\nA. The university raises tuition.\nB. The governor approves of it.\nC. The board of trustees recommends it.\nD. None of the above\nAnswer:", " The governor approves of it."], ["Question: Identify the antecedent of the following conditional proposition: The university raises tuition if, and only if, both the governor approves of it and the board of trustees recommends it.\nChoices:\nA. The university raises tuition.\nB. The governor approves of it.\nC. The board of trustees recommends it.\nD. None of the above\nAnswer:", " The board of trustees recommends it."], ["Question: Identify the antecedent of the following conditional proposition: The university raises tuition if, and only if, both the governor approves of it and the board of trustees recommends it.\nChoices:\nA. The university raises tuition.\nB. The governor approves of it.\nC. The board of trustees recommends it.\nD. None of the above\nAnswer:", " None of the above"], ["Question:  Use the following key to translate the given formula of PL to natural, English sentences.\nA: Marina reads a Percy Jackson book.\nB: Izzy plays Minecraft.\nC: Emily stops working.\nD: Russell makes dinner.\nE: Ashleigh stops by.\n~C \u2228 D\nChoices:\nA. If Emily doesn't stop working then Russell makes dinner.\nB. Emily stops working unless Russell makes dinner.\nC. Emily stops working unless Russell doesn't make dinner.\nD. Emily doesn't stop working unless Russell makes dinner.\nAnswer:", " If Emily doesn't stop working then Russell makes dinner."], ["Question:  Use the following key to translate the given formula of PL to natural, English sentences.\nA: Marina reads a Percy Jackson book.\nB: Izzy plays Minecraft.\nC: Emily stops working.\nD: Russell makes dinner.\nE: Ashleigh stops by.\n~C \u2228 D\nChoices:\nA. If Emily doesn't stop working then Russell makes dinner.\nB. Emily stops working unless Russell makes dinner.\nC. Emily stops working unless Russell doesn't make dinner.\nD. Emily doesn't stop working unless Russell makes dinner.\nAnswer:", " Emily stops working unless Russell makes dinner."], ["Question:  Use the following key to translate the given formula of PL to natural, English sentences.\nA: Marina reads a Percy Jackson book.\nB: Izzy plays Minecraft.\nC: Emily stops working.\nD: Russell makes dinner.\nE: Ashleigh stops by.\n~C \u2228 D\nChoices:\nA. If Emily doesn't stop working then Russell makes dinner.\nB. Emily stops working unless Russell makes dinner.\nC. Emily stops working unless Russell doesn't make dinner.\nD. Emily doesn't stop working unless Russell makes dinner.\nAnswer:", " Emily stops working unless Russell doesn't make dinner."], ["Question:  Use the following key to translate the given formula of PL to natural, English sentences.\nA: Marina reads a Percy Jackson book.\nB: Izzy plays Minecraft.\nC: Emily stops working.\nD: Russell makes dinner.\nE: Ashleigh stops by.\n~C \u2228 D\nChoices:\nA. If Emily doesn't stop working then Russell makes dinner.\nB. Emily stops working unless Russell makes dinner.\nC. Emily stops working unless Russell doesn't make dinner.\nD. Emily doesn't stop working unless Russell makes dinner.\nAnswer:", " Emily doesn't stop working unless Russell makes dinner."], ["Question:  Select the best English interpretation of the given arguments in predicate logic.\nWn \u2228 Wm\n(\u2200x)[Lx \u2283 (Dx \u2283 ~Wx)]\nLn \u2022 Dn\t/ ~(\u2200x)~Wx\nChoices:\nA. 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.\nB. 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.\nC. 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.\nD. 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.\nAnswer:", " 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."], ["Question:  Select the best English interpretation of the given arguments in predicate logic.\nWn \u2228 Wm\n(\u2200x)[Lx \u2283 (Dx \u2283 ~Wx)]\nLn \u2022 Dn\t/ ~(\u2200x)~Wx\nChoices:\nA. 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.\nB. 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.\nC. 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.\nD. 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.\nAnswer:", " 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."], ["Question:  Select the best English interpretation of the given arguments in predicate logic.\nWn \u2228 Wm\n(\u2200x)[Lx \u2283 (Dx \u2283 ~Wx)]\nLn \u2022 Dn\t/ ~(\u2200x)~Wx\nChoices:\nA. 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.\nB. 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.\nC. 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.\nD. 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.\nAnswer:", " 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."], ["Question:  Select the best English interpretation of the given arguments in predicate logic.\nWn \u2228 Wm\n(\u2200x)[Lx \u2283 (Dx \u2283 ~Wx)]\nLn \u2022 Dn\t/ ~(\u2200x)~Wx\nChoices:\nA. 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.\nB. 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.\nC. 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.\nD. 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.\nAnswer:", " 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."], ["Question: Identify the conclusion of the following argument. Remember to remove any conclusion indicators. It is wrong for society to kill a murderer. This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer. And a murderer is wrong in killing his victim.\nChoices:\nA. It is wrong for society to kill a murderer.\nB. This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer.\nC. If a murderer is wrong in killing his victim, then society is also wrong in killing the murderer.\nD. And a murderer is wrong in killing his victim.\nAnswer:", " It is wrong for society to kill a murderer."], ["Question: Identify the conclusion of the following argument. Remember to remove any conclusion indicators. It is wrong for society to kill a murderer. This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer. And a murderer is wrong in killing his victim.\nChoices:\nA. It is wrong for society to kill a murderer.\nB. This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer.\nC. If a murderer is wrong in killing his victim, then society is also wrong in killing the murderer.\nD. And a murderer is wrong in killing his victim.\nAnswer:", " This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer."], ["Question: Identify the conclusion of the following argument. Remember to remove any conclusion indicators. It is wrong for society to kill a murderer. This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer. And a murderer is wrong in killing his victim.\nChoices:\nA. It is wrong for society to kill a murderer.\nB. This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer.\nC. If a murderer is wrong in killing his victim, then society is also wrong in killing the murderer.\nD. And a murderer is wrong in killing his victim.\nAnswer:", " If a murderer is wrong in killing his victim, then society is also wrong in killing the murderer."], ["Question: Identify the conclusion of the following argument. Remember to remove any conclusion indicators. It is wrong for society to kill a murderer. This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer. And a murderer is wrong in killing his victim.\nChoices:\nA. It is wrong for society to kill a murderer.\nB. This follows for the reason that if a murderer is wrong in killing his victim, then society is also wrong in killing the murderer.\nC. If a murderer is wrong in killing his victim, then society is also wrong in killing the murderer.\nD. And a murderer is wrong in killing his victim.\nAnswer:", " And a murderer is wrong in killing his victim."], ["Question:  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)\nChoices:\nA. (\u2200x)(\u2203y)[(Cx \u2022 Sy) \u2022 Gxy)\nB. (\u2200x)[Sx \u2283 (\u2203y)(Cy \u2022 Gxy)]\nC. (\u2200x)[Cx \u2283 (\u2203y)(Sy \u2022 Gxy)]\nD. (\u2200x)[Sx \u2022 (\u2203y)(Cy \u2022 Gxy)]\nAnswer:", " (\u2200x)(\u2203y)[(Cx \u2022 Sy) \u2022 Gxy)"], ["Question:  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)\nChoices:\nA. (\u2200x)(\u2203y)[(Cx \u2022 Sy) \u2022 Gxy)\nB. (\u2200x)[Sx \u2283 (\u2203y)(Cy \u2022 Gxy)]\nC. (\u2200x)[Cx \u2283 (\u2203y)(Sy \u2022 Gxy)]\nD. (\u2200x)[Sx \u2022 (\u2203y)(Cy \u2022 Gxy)]\nAnswer:", " (\u2200x)[Sx \u2283 (\u2203y)(Cy \u2022 Gxy)]"], ["Question:  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)\nChoices:\nA. (\u2200x)(\u2203y)[(Cx \u2022 Sy) \u2022 Gxy)\nB. (\u2200x)[Sx \u2283 (\u2203y)(Cy \u2022 Gxy)]\nC. (\u2200x)[Cx \u2283 (\u2203y)(Sy \u2022 Gxy)]\nD. (\u2200x)[Sx \u2022 (\u2203y)(Cy \u2022 Gxy)]\nAnswer:", " (\u2200x)[Cx \u2283 (\u2203y)(Sy \u2022 Gxy)]"], ["Question:  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)\nChoices:\nA. (\u2200x)(\u2203y)[(Cx \u2022 Sy) \u2022 Gxy)\nB. (\u2200x)[Sx \u2283 (\u2203y)(Cy \u2022 Gxy)]\nC. (\u2200x)[Cx \u2283 (\u2203y)(Sy \u2022 Gxy)]\nD. (\u2200x)[Sx \u2022 (\u2203y)(Cy \u2022 Gxy)]\nAnswer:", " (\u2200x)[Sx \u2022 (\u2203y)(Cy \u2022 Gxy)]"]]