Q17 of 18 Page 13

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.


(i) p: If all angles of a triangle are equal then the triangle is an obtuse angled triangle. Let an angle of a triangle be 90° + θ (obtuse angle)

Now sum of the angles of a triangle is 3(90 + θ ) = 270 + 3θ which is greater than 180° .

Hence a triangle having equal angles cannot be obtuse angled triangle.

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

The equation x2 – 1 = 0 has the root x = 1 which lies between 0 and 2. Hence the given statement is not true.

More from this chapter

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14
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.

15
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.

16
Show that the following statement is true by the method of contra positive.

18
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 bisects 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: is a rational number.