Misc 6 - Check validity of statements given below by - Miscellaneous

Misc  6 - Chapter 14 Class 11 Mathematical Reasoning - Part 2

 

 

  1. Chapter 14 Class 11 Mathematical Reasoning (Deleted)
  2. Serial order wise

Transcript

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.

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.