if `P(n)` be the statement `10n+3` is a prime number", then prove that P(1) and P(2) are true but P(3) is false.

P(n) is the statement : "n^2-n+7 is a prime number"(i)Verify that P(1),P(2),P(3) and P(4) are true.

Let P(n) be the statement : 10n + 3 is prime. Is P(3) true ?

If P(n) is the statement n(n+1)(n+2) is divisiblé by 12, prove that P(3) and P(4) are true, but P(5) is not true

Let P(n) be the statement " n^2-n+41 " is prime. Prove that P(1), P(2) and P(3) are true. Also prove that P(41) is not true. How does this not contradict the Principle of Induction ?

If P (n) is the statement : "n (n + 1) (n + 2) is divisible by 12”, prove that P(3) and P(4) are true, but P(5) is not true.

If P(n) is the statement n^(2)-n+41 is prime. Prove that P(1),P(2) and P(3) are true. Prove also that P(41) is not true.

Let P (n) denote the statement : “ 2^n gen ! ". Show that P(1), P(2) and P(3) are true but P(4) is not true.

If P(n) is the statement n^2-n+41 is prime. Prove that P(1),\ P(2)a n d\ P(3) are true. Prove also that P(41) is not true.

If P (n) is the statement : "2^(3n)- 1 is an integral multiple of 7”, prove that P(1), P(2) and P (3) are true.

Let P(n) be the statement ‘‘4^n > n’’ . If P(r) is true, prove that P(r +1) is also true.