1. [4 marks Truth tables and formulas. Consider the following formula: (a) 2 marks] Write the truth table for the formula. (No need to show your calculations) (b) [2 marks] Write a logically equivalent formula that doesn't use or , in other words it uses only A, v, or . Show how you derived the result 2. [10 marks] congruence Find a natural number m congruent to 5 (mod 7), and another natural number n congruent to 2 (mod 7) Find what the product mn is congruent to (mod 7), and then make a statement about the congruence of the product of any pairs of natural numbers that have the same congruences as the m and n you found, (mod 7) (a) 5 marks] Write a predicate formula that expresses your statement in the form of a universally quantified implication. If you believe the statement, prove it true. If you disbelieve the statement prove it false. (b) [5 marks Write the converse of your formula from the previous part. If you believe the converse, prove it true. If you disbelieve the converse, prove it false