5. Determine whether the following statements are true or false. If they are false, give a counterexample. If they are true, be prepared to prove the statement true by the principle of mathematical induction.
(a) n²-n+11 is prime for all natural numbers n.
(b) n²>n for n>2
(c) 222n+¹ is divisible by 3 for all natural numbers n. n>{n+1)
(d)n3>(n=1)2 for all natural numbers n>2.
(e) n3-n is divisible by 3 for all natural numbers n>2.
(f) n²-6n² +11n is divisible by 6 for all natural numbers n.