Let "Closure of a Relation R with respect to a Property P" be defined as follows:

let R be a relation on a set A. Then a relation R' is the closure of the relation R with respect to property P if and only if

1. R' satisfy the property P, and

2. , and

3. for any(every) relation R'' if and satisfies the property R, then

i.e if there is a relation R' with property P containing R such that R' is a subset of every relation R'' with property P containing R, then R' is called the closure of R with repect to P

Consider the following statements :

1. The reflexive closure R' of a relation R can be obtained as :

R' = , where

2. The symmetric closure R’ of a relation R can be obtained as :

, where

3. The transitive closure R' of a relation R can be obtained as :

, where

4. The symmetric closure R' of a relation R can be obtained as :

, where

Which of the above statements are correct ?

(A). Only 1

(B). Only 1,4

(C). Only 1,2,4

(D). All