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 x2 – 1 = 0 does not have a root lying between 0 and 2.

Asked by Pragya Singh | 11 months ago |  73

1 Answer

Solution :-

(i) The given statement is of the form ‘if q then r’.

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 ~ r.

To prove this, the angles of a triangle are required such that none of them is an obtuse angle.

We know that the sum of all angles of a triangle is 180°.

Therefore, if all the three angles are equal, then each of them is of measure 60°, 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

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

This statement has to be proved false

To show this, let us consider,

x2 – 1 = 0

x2 = 1

x = ± 1

One root of the equation x2 – 1 = 0, i.e. the root x = 1, lies between 0 and 2

Therefore, the given statement is false.

Answered by Abhisek | 11 months ago

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