Write the converse of the following statements.
(i) If a number n is even, then `n^(2)` is even.
(ii) If you do all the exercises in the book, you get an A grade in the class.
(iii) If two integers a and b are such that `a gt b`, then `a -b` is always a positive integer.

Write each of the following statements in the form ''if-then'' To get an A^(+) in the class, it is necessary that you do all the exercises of the book.

Write the negation of the following statements: (i) p: For every real number x, x^(2)gtx . (ii) q: There exists a rational number x such that x^(2) = 2 . (iii) r: All birds have wings. (iv) s: All students study mathematics at the elementary level.

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

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (a) If you live in Delhi, then you have winter clothes. (i) If you do not have winter clothes, then you do not live in Delhi. (ii) If you have winter clothes, then you live in Delhi.

State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If P= {m, n} and Q = {n, m}, then P xx Q= {(m, n),(n, m)}. (ii) If A and B are non-empty sets, then A xx B is a non-empty set of ordered pairs (x, y) such that x in A and y in B. (iii) If A={1,2}, B={3,4} then A xx (B cap phi)=phi

Write each of the following in the form of ax + by + c = 0 and find the values of a, b and c (i) x = -5 (ii) y = 2 (iii) 2x = 3 (iv) 5y = -3

In each of the following questions, we ask you to prove a statement. List all the steps in each proof, ang give the reason for each step. 5. If a and b positive integers, then you know that a =bq +r, 0 £ r lt b , where q is a whole number. Prove that HCF (a,b) =HCF (b,r).

State whether the following statements are true or false, Justify. (i) For an arbitrary binary operation ** on a set N, a**a =a AA a in N. (ii) If ** is a commutative binary opertion on N, then a ** (b **c) = (c**b) **a

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): 4sqrtx-2

Express the following statements using symbols. (i) The element 'x' does not belong to 'A'. (ii) d' is an element of the set 'B'. (iii) 'I' belongs to the set of Natural numbers. (iv) '8' does not belong to the set of prime numbers P.