Using the words ''necessary and sufficient'' rewrite the statement ''The integer n is odd if and only if `n^(2)` is odd''.

Using the words " necessary and sufficient " rewrite the following two biconditional statements : The integer N is even if and only if N^(2) is even .

Prove that if x is odd , then x^(2) is also odd.

Find the first raw moment of first n odd numbers.

Two pairs of statements p and q are given below . Combine theses two statements using the biconditional phrase "if and only if " . p : If the sum of digits in a positive integer n is divisible by 9 , then the number is divisibel by 9 q : If a positive integer n is divisible by 9 , then the sum of the digits in n is divisible by 9 .

Write the converse of each of the following conditional statements : If a number N is odd then N^(2) is odd .

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

If n is an odd positive integer then intabs(x^n) dx is equal to

The S.D. of the first n odd integers is sqrt(85) , find n.

The standard deviation of the first n odd positive integers is sqrt85 find n.

A function f from the set of natural numbers N to the set of integers Z is defined by f(n)={((n-1)/(2),"when n is odd"),(-(n)/(2),"when n is even"):} Then f(n) is -