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 $2$ .

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

x^{2} - 1

= 0

does not have a root lying between

0

and

2

.

Filo · Accepted Answer

(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

\sim r

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

18 0^{\circ}

. Therefore if all the three angles are equal then each of them is of measure

6 0^{\circ}

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,
q : The equation

x^{2} - 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.
Consider

x^{2} - 1 = 0

x^{2} = 1

x = \pm 1

One root of the equation

x^{2} - 1 = 0

i.e., the root

x = 1

lies between

0

and

2

.
Thus the given statement is false.

Question Text	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 $2$ .
Answer Type	Text solution:1
Upvotes	150

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 $2$ .

Text solutionVerified

Practice questions from similar books

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.

Text solutionVerified

Practice questions from similar books

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 $2$ .