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

**Which of the following is False ?**

(A). For any non-empty relation R on a non-empty set A, reflexive closure i.e. closure of R with respect to property “reflexivity”, can always exist.

(B). For any non-empty relation R on a non-empty set A, symmetric closure i.e. closure of R with respect to property “symmetricity”, can always exist.

(C). For any non-empty relation R on a non-empty set A, irreflexive closure i.e. closure of R with respect to property “irreflexivity”, can always exist.

(D). For any non-empty relation R on a non-empty set A, transitive closure i.e. closure of R with respect to property “transitivity”, can always exist.