The given statement can be written in five different ways as follows.

**(i) **A triangle is equiangular implies that is an obtuse-angled triangle.

**(ii) **A triangle is equilateral only if it an obtuse-angled triangle.

**(iii)** For a triangle to be equiangular, it is necessary that the triangle is an obtuseangled triangle.

**(iv)** For a triangle to be an obtuse-angled triangle, it is sufficient that the triangle is equiangular.

**(v)** If a triangle is not an obtuse-angled triangle, then the triangle is not equiangular.

Determine whether the argument used to check the validity of the following statement is correct: p: “If x^{2} is irrational, then x is rational.” The statement is true because the number x^{2} = π^{2} is irrational, therefore x = π is irrational.

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.

**(v)** t: \( \sqrt{11}\) is a rational number.

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.”

Show that the following statement is true “The integer n is even if and only if n^{2} is even”

Show that the following statement is true by the method of the contrapositive p: “If x is an integer and x^{2} is odd, then x is also odd.”