2. for each of the following statements, determine whether the statement is true or false. for a true statement, give a proof. for a false statement, write out its negation and prove that. (a) for all rational numbers a, there is a positive integer n so that na is an integer. (b) there is a positive integer n so that for all rational numbers a, nz is an integer. (c) for all integers a, b and c, if a b + 2c and a | 2b+3c then a | b and a | c (d) for all integers a, b and c, if a l b + 2c and a l 3b + 2c then a | b and a l c.