Determine if the argument is valid or invalid. give a reason to

1. Let p, q, and r be the following statements: p: Jamie is on the train. q: Sylvia is at the park. r: Nigel is in the car. Translate the following statement into English: (~q ^ r) –> ~p 

2. Determine which, if any, of the three statements are equivalent. I) If there is no food left on the table, then we have had dinner. II) If we have had dinner, then there is no food left on the table. III) If there is food left on the table, then we have not had dinner. I, II, and III are equivalent I and II are equivalent II and III are equivalent I and III are equivalent None are equivalent 

3. Determine if the argument is valid or invalid. Give a reason to justify answer. If the bough breaks, then the cradle will fall. The bough breaks. The cradle will fall. Valid by the law of detachment Valid by the law of contrapositive Invalid by fallacy of the converse Invalid by fallacy of the inverse Valid by the law of syllogism Valid by disjunctive syllogism