Please provide the answers for question 2. Thank you.

Translate the following English sentences into statements of predicate calculus. a. All programmers enjoy discrete mathematics Forall = All Programmers Let x "is a programmer" P(x), and "enjoys discrete mathematics" L(x), so P(x) rightarrow L(x) Forall x[P(x) rightarrow L(x)] b. Some integers are not odd Let predicate O(x) meaning "x is an odd integer", and the universe is the set of integers. " " is not the case exist x O(x) c. Every integer that is divisible by 2 is even Let x "is an integer", and x is divisible by 2. Use D for divisible. Use E(x) where x is a even integer. Forall x(exist D[x = 2D]) rightarrow E(x) d. There exists a natural number that is not a positive integer Let N(x) "is a natural number", and P(x) "is a positive integer. " " is not the case exist N(x) P(x) Refer to the statements of predicate calculus you provided for problem 1. Write the negation of each of those statements