Q6 of 134 Page 31

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.”

let us consider a triangle ABC with all angles equal,

Then, each angle of the triangle is equal to 60.

So, ABC is not an obtuse angle triangle.

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

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.”

Show that the following statement is true

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

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) is a rational number.

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.

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.”