1. Given the following statements, determine if they are logically equivalent using a truth table: a.PV (p Aq) =p b.p1qVI) = (p19) VAT) 2. Label each proposition and then rewrite the argument using the logical connectors. Determine if this argument is valid or invalid. a. If I go to the movies, then I won't finish my homework. If I don't finish my homework, then I won't do well on the test tomorrow. Therefore, if I go to the movies, then I won't do well on my test. 3. Use the set of conditional laws to verify the logical equivalences: (p+q)^(pVg) = 9 4. State which rule of inference is the basis of the following argument: "It is below freezing and raining now. Therefore, it is below freezing now." 5. State which rule of inference is used in the argument: If it rains today, then we will not have a barbecue today. If we do not have a barbecue today, then we will have a barbecue tomorrow. Therefore, if it rains today, then we will have a barbecue tomorrow. 6. Show that the premises "If you send me an e-mail message, then I will finish writing the program," "If you do not send me an e-mail message, then I will go to sleep early," and "If I go to sleep early, then I will wake up feeling refreshed" lead to the conclusion of I do not finish writing the program, then I will wake up feeling refreshed