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.

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^ngeq3n , and if P(r) is true, prove that P(r+1) is true.

Prove that P(n,n) = P(n,n-1)

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

If P(n) is the statement n^3+n is divisible by 3, prove that P(3) is true but P(4) is not true.

Let P(n) be the statement ''(3)^(n)gt n'' . If P(n) is true , prove that P(n + 1) is true.

If P(n) be the statement 2^ngtn^n and if P(m) is true, show tht P(m+1) is also true

If P(n) is the statement n(n+1) is even, then what is P(3)?

If P(n) is the statement "2^(3n)-1 . Is an integral multiple 7", and if P(r) is true, prove that P(r+1) is true.

Let P(n) be the statement: 2^n >= 3n . If P(r) is true, show that P (r + 1) is true. Do you conclude that P(n) is true for all n in N