1. [-12 Points] DETAILS SMITHNM13 3.4.005. Determine whether each argument is valid or invalid. Give reasons for your answer. (a) p q ~q .. ~p O valid by direct reasoning O valid by indirect reasoning O valid by the law of the excluded middle 0 invalid by the fallacy of the converse O invalid by the fallacy of the inverse (b) p > a q '. p O valid by direct reasoning O valid by indirect reasoning O valid by the law of the excluded middle 0 invalid by the fallacy of the converse O invalid by the fallacy of the inverse Need Help? ' 2. [-I2 Points] DETAILS SMITHNM13 3.4.007. I: Determine whether each argument is valid or invalid. Give reasons for your answer. (a peq \"P '. ~q O valid by direct reasoning O valid by indirect reasoning O valid by the law of the excluded middle 0 invalid by the fallacy of the converse O invalid by the fallacy of the inverse (b) p > q p .. q 0 valid by direct reasoning O valid by indirect reasoning O valid by the law of the excluded middle 0 invalid by the fallacy of the converse O invalid by the fallacy of the inverse Need Help? .2311- 3. [-11 Points] DETAILS SMITHNM13 3.4.009. MY NOTES ASK YOUR TEACHER Determine whether the argument is valid or invalid. If valid, name the type of reasoning, and if invalid, determine the error in reasoning. IfI inherit $1,000, I will buy you a cookie. I inherit $1,000. Therefore, I will buy you a cookie. O valid; direct reasoning O valid; indirect reasoning O valid; transitive reasoning O invalid; false chain pattern 0 invalid; fallacy of the inverse Need Help? _' 5. [-11 Points] DETAILS SMITHNM13 3.4.015. MY NOTES ASK YOUR TEACHER Determine whether the argument is valid or invalid. If valid, name the type of reasoning, and if invalid, determine the error in reasoning. 1f Congress appropriates the money, the project can be completed. Congress appropriates the money. Therefore, the project can be completed. 0 valid; direct reasoning O valid; indirect reasoning O valid; transitive reasoning O invalid; false chain pattern 0 invalid; fallacy of the inverse Need Help? _' 6. [-11 Points] DETAILS SMITHNM13 3.4.017. MY NOTES ASK YOUR TEACHER Determine whether the argument is valid or invalid. If valid, name the type of reasoning, and if invalid, determine the error in reasoning. Blue-chip stocks are safe investments. Stocks that pay a high rate of interest are safe investments. Therefore, blue-chip stocks pay a high rate of interest. 0 valid; direct reasoning O valid; indirect reasoning O valid; transitive reasoning O invalid; false chain pattern 0 invalid; fallacy of the inverse Need Help? _' 7. [I1 Points] DETAILS SMITHNM13 3.4.018. MY NOTES ASK YOUR TEACHER Determine whether the argument is valid or invalid. If valid, name the type of reasoning, and if invalid, determine the error in reasoning. If AI understands logic, then he enjoys this sort of problem. Al does not understand logic. Therefore, Al does not enjoy this sort of problem. 0 valid; direct reasoning O valid; indirect reasoning O valid; transitive reasoning O invalid; false chain pattern 0 invalid; fallacy of the inverse Need Help? _ 8. [-I1 Points] DETAILS SMITHNM13 3.4.021. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Determine whether the argument is valid or invalid. If valid, name the type of reasoning, and if invalid, determine the error in reasoning. If2x 10 = 0,thenx= 5. x at 5 Therefore, 2X 10 0. O valid; direct reasoning O valid; indirect reasoning O valid; transitive reasoning O invalid; false chain pattern 0 invalid; fallacy of the inverse 9. [-I1 Points] DETAILS SMITHNM13 3.4.023. | MY NOTES Determine whether the argument is valid or invalid. If valid, name the type of reasoning, and if invalid, determine the error in reasoning. If Ron uses Slippery oil, then his car is in good running condition. Ron's car is in good running condition. Therefore, Ron uses Slippery oil. 0 valid; direct reasoning O valid; indirect reasoning O invalid; false chain pattern 0 invalid; fallacy of the converse O invalid; fallacy of the inverse Need Help? 10. {-11 Points] DETAILS SMITHNM13 3.4.029. | MY NOTES Use a symbolic argument to determine if the argument is valid or invalid. All mathematicians are eccentrics. All eccentrics are rich. Therefore, all mathematicians are rich. O valid 0 invalid Need Help? _' 11. [-I1 Points] DETAILS SMITHNM13 3.4.030. | MY NOTES Use a symbolic argument to determine if the argument is valid or invalid. No students are enthusiastic. You are enthusiastic. Therefore, you are not a student. 0 valid O invalid 12. [-72 POIS] DETAILS SMITHINITS 3.4.057. Form a valid conclusion, using all the premises given for the argument. If you learn mathematics, then you are intelligent. If you are intelligent, then you understand human nature. If you understand human nature, then you have learned mathematics. If you learn mathematics, then you do not understand human nature. If you learn mathematics, then you understand human nature. If you do not learn mathematics, then you do not understand human nature. O If you do not understand human nature, then you are not intelligent. Give reasons for your answer. O A valid conclusion is formed by using direct reasoning. O A valid conclusion is formed by using indirect reasoning. O A valid conclusion is formed by using transitive reasoning. O A valid conclusion is formed by using the law of the excluded middle. O A valid conclusion is formed by using the law of contraposition. Need Help? Read It 13. [-/2 Points] DETAILS SMITHNM13 3.4.042. Form a valid conclusion, using all the premises given for the argument. If a . b = 0, then a = 0 or b = 0. a . b = 0 O a # 0 orb # 0 O a = 0 orb = 0 O a = 0 and b = 0 Ob + 0 O a = 0 Give reasons for your answer. O A valid conclusion is formed by using direct reasoning. O A valid conclusion is formed by using indirect reasoning. O A valid conclusion is formed by using transitive reasoning. O A valid conclusion is formed by using the law of the excluded middle. O A valid conclusion is formed by using the law of contraposition.14. [-IZ Points] DETAILS SMITHNM13 3.4.046. Form a valid conclusion, using all the premises given for the argument. If 2 divides a positive integer N and if N is greater than 2, then N is not a prime number. N is a prime number. 0 Two does divide a positive integer N or N is greater than 2. 0 Two does not divide a positive integer N or N is not greater than 2. O N is not greater than 2. 0 Two does not divide a positive integer N. 0 Two does divide a positive integer N and N is greater than 2. Give reasons for your answer. Q A valid conclusion is formed by using direct reasoning. O A valid conclusion is formed by using indirect reasoning. O A valid conclusion is formed by using transitive reasoning. O A valid conclusion is formed by using the law of the excluded middle. 0 A valid conclusion is formed by using the law of contraposition. Need Help? _