Identify the quantifier in the following statements and write the negation of the statements.
(i) There exists a number which is equal to its square.
(ii) For every real number $x, x$ is less than $x+1$.
(iii) There exists a capital for every state in India.

Answer

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Geometry

NCERT Class 11 - Math

Chapter 14

Mathematical Reasoning

Section 3

New Statements from Old

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Video Transcript

in this problem, let us first look at the first sentence which is there exists number which is equal to its square, identify the quantify here. Is there exists next? The negation of this statement will be there does not exist a number which is equal to its square, so there does not exist a number. And whatever the sentence after next is for every real number X. X is less than X plus one. The identity the quantified here is for every. And the negation of which will be. There exist a real number X. Such that X is not Place the next plus one. So there exists a real number X. Such that X. S not nurse thing express one. For the third centers, there exists the capital for every state in new york quantify res there exists and negation will be that there exists a state in India which does not have a capital. So there exists or state in India. Rich does not. Uh huh. Captain, that's

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