Check the validity of the statements given below by the method given against it.
(i) p: The sum of an irrational number and a rational number is irrational (by contradiction method).
(ii) q: If n is a real number with `n gt 3`, then `n^(2)gt9` (by contradiction method).

Find the component statements of the following and check whether they are true or not. sqrt2 is a rational number or an irrational number.

Find any five rational numbers between 2 and 3 using mean method.

Identify the type of ''Or'' used in the following statements and check whether the statements are true or false: sqrt2 is a rational number or an irrational number

If tantheta=sqrt n , where n in N, >= 2 , then sec2theta is always (a) a rational number (b) an irrational number (c) a positive integer (d) a negative integer

If (log)_a x=b for permissible values of a and x , then identify the statement(s) which can be correct. (a)If a and b are two irrational numbers, then x can be rational. (b)If a is rational and b is irrational, then x can be rational. (c)If a is irrational and b is rational, then x can be rational. (d)if aa n d b are rational, then x can be rational.

Find the sum of: (i) the first 1000 natural numbers, (ii) the first n natural numbers.

The sum of all natural numbers 'n' such that 100 lt n lt 200 and HCF (91, n) gt 1 is

Solve 3x+8 gt2 , when (i) x is an integer. (ii) x is a real number.

Check whether the statement if x and y are odd integers, then xy is an odd integer is true or false by i. direct method ii. Contrapositive method. iii. Contradiction method.

If x^2 + 2x + n gt 10 for all real number x, then which of the following conditions is true ?