please help with 22, 24, 26

15. Something is rotten in the state of Denmark, or my name isn't Hamlet. My name is Hamlet. Something is rotten in the state of Denmark. 16. "We shall conquer together or we shall die together." (quote from Winston Churchill) We shall not die together. We shall conquer together. Determine whether each argument is valid or invalid. If it is valid, give a proof. If it is invalid, give an assignment of truth values to the variables that makes the premises true and the conclusion false. 17. p V q P ~9 19. p q 9 p p^ q 21. ~p~9 9 P 23. p q ~9 ~Pr 25. p q qr ~P 27. p q q~r P rvs 18. p V ~q P ~q 20.-p-9 P ~q 22. p~9 9 ~P 24. pv q ~P r~q 26. p q r~q P~r 28. p q ~pr s~q ~r~s p^ q 38. Explain in your own words what distinguishes a valid argument form from an invalid argument form. Applications For Exercises 39-47, determine whether each of the following arguments is valid or invalid. If it is valid, give a proof. If it is invalid, give an assignment of truth values to the variables that makes the premises true and the conclusion false. Business and Economics 39. Investment If Alex invests in AT&T, Sophia will invest in Sprint Nextel. Victor will invest in Verizon or Alex invests in AT&T. Victor will not invest in Verizon. Therefore, Sophia will invest in Sprint Nextel. 40. Credit If you make your debt payments late, you will dam- age your credit record. If you damage your credit record, you will have trouble getting a loan. You do not have trouble getting a loan. Therefore, you do not make your debt pay- ments late. 41. Stock Market It is a bearish market. If prices are rising, then it is not a bearish market. If prices are not rising, then the investor will sell stocks. Therefore, the investor will not sell stocks. Life and Health Sciences 42. Classification If the animal is a reptile, then it belongs to the chordate phylum. The animal either belongs to the echinoderm phylum or the chordate phylum. It does not belong to the echi- noderm phylum. Therefore, it is not a reptile. 43. Classification The animal is a spider or it is an insect. If it is a spider, then it has eight legs and it has two main body parts. It does not have eight legs or it does not have two main body parts. Therefore, it is an insect. Social Sciences 44. Politics If Bahwaini runs for senator, then Haney will run for governor. If Toussant runs for state representative, then Haney will not run for governor. Therefore, if Toussant runs for state representative, then Bahwaini will not run for senator