Determine whether the argument used to check the validity of the following statement is correct: p: “If x² is irrational, then x is rational.” The statement is true because the number x² = π² 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 n² is even”

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.”