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.

If P(n) is the statement 4n<2^n (i)Verify that P(1),P(2),P(3),P(4) and P(5) are true.

P(n) is the statement : "n^2-n+7 is a prime number"(ii)Can you say that P(n) will be true for all natural numbers?give reason.

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

If P(n) is the statement n(n+1) is even then what about P(6)?

Let P(n) denotes the statement '3^n gt 2^n' . Is P(1) true?

Consider the statement '' 10^(2n-1)+1 is divisible by 11''. Verify that P(1) is true and prove the statement by using mathematical induction.

Let P(n) denotes the statement n^3+(n+1)^3+(n+2)^3 is a multiple of 9 Prove that P(1) is true

Consider the statement P(n):7^n-3^n is divisible by 4. Show that P(1) is true.

If P(n) is the statement '4n<2^n'(iii)If P(K) is true,show that P(K+1) is true for Kge5 .

Let P(n) denotes the statement 2^n gt n and if P(n) is true, show that P(n+1) is also true