Determine whether the given statement is true or false. justify. a) there exists a positive integer n such that+5n is prime. b) there exists a positive integer n such that +5n + 8 is prime. c) there exists a positive integer n such that n+ 5n+9 is prime. d) there exists infinitely many positive integers n such that+57 is composite. e) for all positive integers n, n+21n+ 1 is prime.