Exercise 14.5

Which of the following statements are true and which are false? In each case give a valid reason for saying so. (i) r: Circle is a particular case of an ellipse. (ii) s: If x and y are integers such that x > y, then –x < –y.

(i) The condition of an elipse is, In the event that we put\[~a\text{ }=\text{ }b\text{ }=\text{ }1\], we get \[{{x}^{2}}~+\text{ }{{y}^{2}}~=\text{ }1,~\], which is a condition of a circle Thus,...

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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 bisects each chord of the circle.

(I) The given assertion \[p\]is bogus. By the meaning of harmony, it ought to meet the circle at two particular focuses (ii) The given assertion \[q\]is bogus. The middle won't cut up that harmony...

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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.

(I) Let \[q:\]All the points of a triangle are equivalent \[r:\]The triangle is an insensitive calculated triangle The given assertion \[p\]must be refuted. To show this, required points of a...

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