For my discrete mathematical structures for computer science class.

2. If p V q is a sufficient condition for r, and r is a necessary condition for q, can p be logicaly concluded if we know -q is the case? In other words, is it valid to conclude p? Justify your answer by writing out the statements into an argument form. 3. Which of the following is a negation for "Jim has grown or Joan has shrunk." a. Jim has grown or Joan has shrunk b. Jim has grown or Joan has not shrunk. c. Jim has not grown or Joan has not shrunk. d. Jim has grown and Joan has shrunk. e. Jim has not grown and Joan has not shrunk f. Jim has grown and Joan has not shrunk