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. Write the inverse, converse, and contrapositives of "If I never eat, then I never have to brush my teeth." 4. Write the inverse, converse, and contrapositives of "If I am not in jail, then I did not rob a bank." 5. Write the inverse, converse, and contrapositives of "If a village has an orange tree, then the villagers eat oranges." 6. Rewrite the following statement in if-then form without using the word necessary: Getting an answer of 10 for problem 16 is a necessary condition for solving problem 16 correctly. 7. If the condition p is necessary for q, which statement is logically equivalent: p if q, or p only if q? 8. Determine whether the following argument is valid or invalid. Include a truth table and a few words explaining why the truth table shows validity or invalidity. If Hugo is a physics major or if Hugo is a math major, then he needs to take calculus Hugo needs to take calculus or Hugo is a math major Therefore, Hugo is a physics major or Hugo is a math major