if R1 is irreflexive and R2 is irreflexive then can R1 union R2 be reflexive ? true or false

Question

if R1 is irreflexive and R2 is irreflexive  then can R1$\cup$ R2 be reflexive ? true or false

Comments

Reflexive under what ??

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suppose any set take it a{1,2,3}

Answer 1

FALSE.

If relations R1 and R2 are irreflexive, then the relations R1 U R2, R1 ⋂ R2, R1^-1 are also Irreflexive.

Comments

no matter all are not present na.. then it would be definitely irreflexive if in R1 one selfloop (3,3) will be present then it wonn't be irreflexive

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no... if even it contains a single self loop also it is not an irreflexive relation.... please take correct example... your approach is wrong.

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srry u r right , srry to make  u annoying  :(

Answer 2

TRUE

let set A{1,2,3} then R1{(2,3),(1,2),} irreflexive , also R2{(2,1),(3,2)} is also irreflexive .

when, R1$\cup$R2 ={(2,1),(2,3),(1,2),(3,2)} is also irreflexive

so given statement is true

Comments

Yes. Union, Intersection and Inverse of an irreflexive relation does not contain any self loops. That's why it is always irreflexive.

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thanks alot

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thank you