Question

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  does not have a root lying between and .

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Solution

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(i) The given statement is of the form "if then "
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 then 
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 . Therefore if all the three angles are equal then each of them is of measure  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 is false.
(ii) The given statement is as follows,
q : The equation  does not have a root lying between and .
This statement has to be proved false. To show this a counter example is required.
Consider 


One root of the equation  i.e., the root lies between and .
Thus the given statement is false.

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Solution to Question ID 418295
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