Reflexive Relation

Question

Can anyone help …. where I am wrong…??

Comments

Reflexive closure : It should satisfy three condition 

1. It should be reflexive 
2. It should contains R
3.  It should be minimal relation satisfy condition a and b

Option a : satisfy condition a but  violate condition b 

Option  b : doesn’t satisfy any of these three condition 

option c : satisfy all three condition 

Answer : only III 

Answer 1

@Vikas123 then reflexive closure is, by the definition of a reflexive closure S of a relation R on a set is given by

since s contain all the pairs (1,1) (2,2) (3,3)  therefore S=R

 

GO THROUGH THIS (HOPE THIS HELPS)

https://en.wikipedia.org/wiki/Reflexive_closure

 

Comments

than how option (1) is wrong...

---

I think option B should be correct because reflexive relation should be {(1,1),(2,2),(3,3)} according to the definition aRa, where a belongs to relation R.

---

according to definition reflexive closure should be union of R and identity elements(diagonal elements) so reflexive closure should contain atleast R plus diagonal elements so thats why option 3 should be correct and option 1 is wrong because it doesn't contain all elements of R.