Show that the statement "For any real number a and b, a² = b² implies that a = b" is not true by giving a counter example.

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

(b)
 (i) If a quadrilateral is a parallelogram, then its diagonals bisect each other.
(ii) If the diagonals of a quadrilateral do not bisect each other, then the
quadrilateral is not a parallelogram.

Show that the statement p: "If x is a real number such that x³ + 4x = 0, then x is 0" is true by

(i) Direct method.

(ii) Method of contradiction.

(iii) Method of contra positive.

Show that the following statement is true by the method of contra positive.

By giving a counter example, show that the following statements are not true.

(i) p: If all the angles of a triangle are equal then the triangle is not obtuse angled triangle.

(ii) q: The equation x² – 1 = 0 does not have root lying between 0 and 2.