Show that the statement
p: ''If x is a real number such that `x^(3) + 4x = 0`, then x is 0'' is true by
(i) direct method, (ii) method of contradiction, (iii) method of contrapositive

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.

Solve 5x-3 lt 3x+1 when (i) x is an integer (ii) x is a real number.

Write the contrapositive and converse of the following statements. If x is a prime number, then x is odd.

Show that the following statement is true by the method of contrapositive. p: If x is an integer and x2 is even, then x is also even.

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 roots of 4x^(2)+3x+5=0 by the method of completing the square.

Write the negation of the following statement: i. p: for every positive real number x, the number x-1 is also positive. ii. q : All cats scratch. r: For every real number x, either x>1 or x iv. s : There exists a number x such that 0ltxlt1 .