Show that the following statement is true

“The integer n is even if and only if n² is even”

Show that the statement

p : “If x is a real number such that x³ + x = 0, then x is 0” is true by

(i) Direct method

(ii) method of contrapositive

(iii) method of contradiction

Show that the following statement is true by the method of the contrapositive

p : “If x is an integer and x² is odd, then x is also odd.”

By giving a counter example, show that the following statement is not true.

p : “If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.”

Which of the following statements are true and which are false? In each case give a valid reason for saying so

(i) p : Each radius of a circle is a chord of the circle.

(ii) q : The centre of a circle bisect each chord of the circle.

(iii) r : Circle is a particular case of an ellipse.

(iv) s : If x and y are integers such that x > y, then – x < - y.