Question

Check whether the relations R in the set of natural number N given by R={(x, y):x is odd and y= 2x} is an equivalence relation.
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Answer 1

Step-by-step explanation:

R={(1,2)(2,4)(3,6)....}

r is not reflexive relation

r is not symmetric relation

r is not transitive relation

so, r is not equivalence relation

Answer 2

Answer:

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Step-by-step explanation:

ANSWER ::

R IS NOT A EQUIVALENCE RELATION

Here N = { 1,2,3,4,5,............}

Now R is not Reflexive

Since every element of R is of the form (x, 2x) where x€ N

1 belongs to N but ( 1, 1) does not belongs to R

Since 1 # 2× 1

So R is not Reflexive

So R is not Equivalence Relation