Rewrite the following statements in the two forms: "Forall X, if _____ then _________" and "Forall ________ X, __________" (without an if-then). Every computer science student needs to take data structures. Rewrite the following statements in the two forms: "Exist _____ x such that _____" and "Exist x such that _______ and _______." Some questions are easy. Rewrite each statement without using quantifiers or variables. Let the domain of x be the set Z of integers, and let Odd(x) be "x is odd, " Prime(x) be "x is prime, " and Square(x) be "x is a perfect square." a) Exist x such that Prime(x) Lambda ~ Odd(x). b) Forall x, Prime(x) rightarrow ~ Square(x). c) Exist x such that Odd(x) Lambda Square(x). Writer the negation, converse, inverse, and contrapositive for the statement. Forall real numbers x, if x>3 then x^2 > 9. Rewrite the statement formally using quantifiers and variables, then write a negation for the statement. a) Any even integer equals twice some integer. b) There is a program that gives the correct answer to every question that is posed to it