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Miscellaneous

Misc 1 (i)
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Misc 6 (i) Important Deleted for CBSE Board 2022 Exams You are here

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Misc 7 Important Deleted for CBSE Board 2022 Exams

Last updated at Aug. 31, 2021 by Teachoo

Misc 6 Check the validity of the statements given below by the method given against it. p: The sum of an irrational number and a rational number is irrational (by contradiction method). (i) The given statement is as follows. p: the sum of an irrational number and a rational number is irrational. Let us assume that the given statement, p, is false. That is, we assume that the sum of an irrational number and a rational number is rational. Therefore, a + b c = d e , where a is irrational and b, c, d, e are integers. d e = b c is a rational number and a is an irrational number. This is a contradiction. Therefore, our assumption is wrong. Therefore, the sum of an irrational number and a rational number is rational. Thus, the given statement is true.