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True/False: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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Q.1. For real numbers x and y, we write x * y if x –y + True/False: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is an irrational number. Then, the relation* is an equivalence relation. (1981 - 2 Marks)

Ans. F

Sol. Given  that, x * y = x –y+True/False: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Consider x = 2True/False: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE , y = True/False: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

then x *y  True/False: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE(irrational)

and y *x =True/False: Miscellaneous (Sets, Relations, Statistics & Mathematical Reasoning) | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE (rational)

∴ x * y ¹ y * x

Hence * is not symm. ⇒ * is not an equivalence relation

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