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 $x^{2}-1=0$ does not have a root lying between 0 and 2 .

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Geometry

NCERT Class 11 - Math

Chapter 14

Mathematical Reasoning

Section 5

Implications

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Video Transcript

by giving a counter example show that the following statement are not true. The statement P is if all the angles of a triangle are equal, then the triangle is an abuse angle triangle. And the answer will be. The given statement is of the form. If you then are now let let the statement QB all the angles of a triangle are equal. And like the statement I'll be, the triangle is an obtuse angle triangle. The given statement he has to be proved falls for this purpose. It has to be proved that if you then the given statement, he has to be proved false for this purpose, it has to be proved that if you then negation are to show this angle for triangular required such that none of them is not abused angle. It is known that to show this angles of a triangle are required such that none of them is an obtuse angle. It is known that some of all the angles of a triangle is vanity degree. Therefore, if all the three angles are equal then each of them is to be measures it's a degree which is not an abuse angle in an equilateral triangle, the measure of all the angle is equal. However, the tangle is not an obtuse angle triangle so it can be concluded that the given statement yeah B. S. Once in part two we have given the statement Q. That is the equation X squared minus one is equal to zero. Does not have a root lying between zero and 2. This statement has to be proved false to show that a counter example is required. Consider x squared minus one is equal to zero, adding one on both sides, adding one on both side. We get X whereas equals to one. So we get Xs equals to plus minus one. Here we have one root of equation X squared minus one is equals to zero. That is the root X. S equals to one that lies between zero and two. Does. The given statement is false.

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