Determine whether the following statement forms are logically equivalent. Construct a truth table and include a sentence to justify your answer (4 pts): ~(qu)and~p A~q p A t andp (t isa tautologicalstatement) Use De Morgan's laws to write negation for the following statement (2 ptsl: The dollar is at an alltime high and the stock market is at a record low. This computer program has a logical error in the first ten lines or it is being run with an incomplete data set. Use Theorem 2.1.1 (reference table) to verify the logical equivalences in the following (2 pts): pA(~qu)Ep Construct a truth table for the following (2 pts), remembering to observe the order of operations discussed in class: q A \"'39 -' 1" Use the logicalequivalencesp > q E~ p V q and p (3 pts): (P -' 7') (q -> 7") Write the following statement in its contrapositive, converse, and inverse forms (3 pts): If x is nonnegative, then x is positive or x is 0