Class XI Chapter 14 – Mathematical Reasoning Maths ______________________________________________________________________________ To prove that q is false, it has to be proved that x is not an integer or 2 x is not even implies that x is also not even. Therefore, statement q is false. Thus, the given statement p is true. 2 x is not even. Question 4: 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 an obtuse angled triangle. (ii) q: The equation 2 x - 1 = 0 does not have a root lying between 0 and 2. Solution 4: (i) The given statement is of the form â€œ if q then r â€. q: All the angles of a triangle are equal. r: The triangle is an obtuse-angled triangle. The given statement p has to be proved false. For this purpose, it has to be proved that if q, then â ¼r. To show this, angles of a triangle are required such that none of them is an obtuse angle. It is known that the sum of all angles of a triangle is 180Â°. Therefore, if all the three angles are equal, then each of them is of measure 60Â°, which is not an obtuse angle. In an equilateral triangle, the measure of all angles is equal. However, the triangle is not an obtuse-angled triangle. Thus, it can be concluded that the given statement p is false. (ii) The given statement is as follows. 2 q: The equation x - 1 = 0 does not have a root lying between 0 and 2. This statement has to be proved false. To show this, a counter example is required. 2 Consider x - 1 = 0 2 x = 1 x = Â± 1 2 One root of the equation x - 1 = 0, i.e. the root x = 1, lies between 0 and 2. Thus, the given statement is false. Question 5: 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. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 14 – Mathematical Reasoning Maths ______________________________________________________________________________ (iii) r: Circle is a particular case of an ellipse. (iv) s: If x and y are integers such that x > y, then â€“x < â€“y. (v) t: **11** is a rational number. Solution 5: (i) The given statement p is false. According to the definition of chord, it should intersect the circle at two distinct points. (ii) The given statement q is false. If the chord is not the diameter of the circle, then the centre will not bisect that chord. In other words, the centre of a circle only bisects the diameter, which is the chord of the circle. (iii) The equation of an ellipse is, 2 2 x y 1 2 2 a b If we put a = b = 1, then we obtain 2 2 x y 1, which is an equation of a circle Therefore, circle is a particular case of an eclipse. Thus, statement r is true. (iv) x > y ⇒ â€“ x < â€“ y (By a rule of inequality) Thus, the given statement s is true. (v) **11** is a prime number and we know that the square root of any prime number is an irrational number. Therefore, **11** is an irrational number. Thus, the given statement t is false. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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