(Solved): Problem 1: Determine whether or not the following two statements, (a) and (b), are logically equiva ...

Problem 1: Determine whether or not the following two statements, (a) and (b), are logically equivalent, (You miay use truth tables or logical properties, but must use some form of formal argument for logical equivalence; the statements as they are should be symbolized before any other argument is made. Make sure to clarify the meaning of any symbols you introduce) (a): Parvati is studying literature and mathematics and Quinn is studying literature, but Quinn is not studying both literature and mathematics. (b) It is not the case that both Parvati and Quinn are both studying literature and mathematics, but it is the case that Quinn is studying literature and Parvati is studying both literature and mathematics. Hint: it is possible to write theselusing only three statement variables. Problem 2: Use the losical equivalences established in Theorem $$2.11$$ as well as the properties of conditional statements to prove that $$(?p??q)??(p?q)??q$$. (Cite each equivalence used, and only use one at a time) Problem 3. Show that the three statements below are all logically equivalent (using equivalences in the same way as Problem 2). (a) $$p?q?r$$ (b) $$p??q?r$$ (c) $$p????q$$