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.

Asked by Pragya Singh | 11 months ago | 73

**(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 x^{2} – 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,

x^{2} – 1 = 0

x^{2} = 1

x = ± 1

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

Therefore, the given statement is false.

Answered by Abhisek | 11 months agoDetermine whether the argument used to check the validity of the following statement is correct: p: “If x^{2} is irrational, then x is rational.” The statement is true because the number x^{2} = π^{2} is irrational, therefore x = π is irrational.

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 bisect each chord of the circle.

**(iii)** r: Circle is a particular case of an ellipse.

**(iv)** s: If x and y are integers such that x > y, then – x < – y.

**(v)** t: \( \sqrt{11}\) is a rational number.

By giving a counter example, show that the following statement is not true. p: “If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.”

Show that the following statement is true “The integer n is even if and only if n^{2} is even”

Show that the following statement is true by the method of the contrapositive p: “If x is an integer and x^{2} is odd, then x is also odd.”