Prove that following statements.
If `n^2` is an even integer, then n is also an even integer.

By giving a counter example, show that the following statement is false. "If n is an odd integer, then n is prime.”

If n is a positive integer, then find int x^n dx

Write the converse of the following statements. If a number x is even, then x^2 is also even.

State the converses of the following statement. In each case, also decide whether the converse is true or false.:- If n is an even integer, then 2n + 1 is an odd integer.

If n is an odd number then n^(3) will be an even number.

Write the set of all integers whose cube is an even integer.

Find counter-examples to disprove the following statement: n^2 -n + 41 is a prime for all positive integers n

Justify the following statements . Sum of a positive integer and a negative integer is always a positive integer.