2. Proofs. In the problems below, start with restating the problem statement using quantifiers. In the proof itself, say when you are using universal/existential instantiation and generalization. State explicitly which definitions you are using and when, and show all proof steps (including algebra). (a) For any real number z, an integer y is called the ceiling of z (written as y = [2]) if and only if it is the smallest integer greater than or equal to 2. i. Write the definition above as a predicate logic formula. Use