Using the words necessary and sufficient rewrite the statement. The integer n is odd if and only if `n^2` is odd Also choice whether the statement is true.

Write the converse of the following statement : If a number n is odd, then n^2 is odd.

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

Statement-1: the highest power of 3 in .^(50)C_(10) is 4. Statement-2: If p is any prime number, then power of p in n! is equal to [n/p]+[n/p^(2)]+[n/p^(3)] + . . ., where [*] denotes the greatest integer function. a. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1 b. Statement-1 is true, statement-2 is true, statement-2 is not a correct explanation for statement-1 c. Statement-1 is true, statement-2 is false d. Statement-1 is false, statement-2 is true

Let P (n) be the statement ''3^n >n'' . Is P (1) true?

Let P(n) be the statement ''n^3 +n is divisible by 3”. Is the statement P(4) true ?

State whether the followin statements are True of False: If an even number is divided by 2,the quotient is always odd.

State whether the following statements are true or false. Equation is also an identity.

Let P(n) be the statement ''n^3 +n is divisible by 3”. Is the statement P( 3) true ?

Check whether the following statement is true or false. All prime numbers are odd.

Let P(n) denote the statement that n^2+n is odd . It is seen that P(n)rArr P(n+1),P(n) is true for all