Let be the set of natural numbers and a relation on be defined by . Then the relation is...

(a) : Reflexive : Let is reflexive. Symmetric : Let So, is not symmetric. Similarly, is not transitive. ...

Let N be the set of natural numbers and a relation R on N be defined by = {(x,y) in N X N:x^{3} - 3x^{2}y - xy^{2} + 3y^{3} = 0}. Then the relation R is: Relation (Mathematics)

Exam ( $27^{th\ }$ July $2^{nd\ }$ Shift 2021)

Mathematics

Let

N

be the set of natural numbers and a relation

R

N

be defined by

= \{(x,y) \in N \times N:x^{3} - 3x^{2}y -

xy^{2} + 3y^{3} = 0\}

. Then the relation

R

reflexive but neither symmetric nor transitive

an equivalence relation

reflexive and symmetric, but not transitive

symmetric but neither reflexive nor transitive

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