By giving a counter example, show that the ...

NCERT Class XI Mathematics - Mathematical Reasoning - Solutions

Question : 17 of 25

Marks: +1, -0

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.

Solution:

(i) Since the triangle is an obtuse angled triangle then q > 90°.

Let q = 100°

Also all the angles of the triangle is equal.

∴ Sum of all angles of the triangle is 300°, which is not possible.

Thus, the given compound statement is not true.

(ii) We see that x = 1 is a root of the equation

x^2

– 1 = 0, which lies between 0 and 2. Thus, the given compound statement is not true.

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