Consider R set of real numbers
Define a relation R1 on R as
R1 = { ( x,y ) / x,y contained in R such that x is greater than or equal to y (square ).
Is R1 a equivalence ??

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Solution

$Dear Student, R_{1} = \{(x, y) : x, y \in R and x \geq y^{2}\} So R_{1} = \{(2, 1), (3, 1), (5, 4), . . . etc\} Here we can see that (1, 1) is not there so it is not symmetric And Also, here condition (x, y) \in R and (y, z) \in R then (x, z) \in R is not satisfying so it is not equvalence Regards$

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