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Ans:B

Symmetric closure of R

1. It is symmetric

2. It contains R

3.Minimal relation satisfying 1 and 2

If we consider B, then condition 2 may be violated. Therefore I think the answer should be D.

 

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The ans is b.

Let's take an example,A={1,2,3,4,6}.

Relation(R) on A ={(a,b):a divides b} or b%a =0. Therefore R={(1,2),(2,4),(3,6)}.

A symmetric closure on R i.e R* should satisfy 3 conditions:-

  1. It should contain R
  2. It should be symmetric
  3. It should be minimal

Therefore R*={(1,2),(2,4),(3,6),(2,1),(4,2),(3,6)} which can be also written as R*={(x,y):either x divides y or y divides x}.

So,(B) is the right option to go for.

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i also think d is correct

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