in Mathematical Logic
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Can anyone help …. where I am wrong…??

in Mathematical Logic
474 views

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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 

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1 Answer

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@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

 

3 Comments

than how option (1) is wrong...
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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.
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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.
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