Prove or disprove If B is a partial order on set A then the

Prove or disprove: If B, is a partial order on set A, then the symmetric closure of R is an equivalence relation.

Solution

Equivalence relations–:

                       A relation that is reflexive, symmetric and transitive

Partial order -: A relation that is reflexive, antisymmetric and transitive

            Let R be a relation on A, and let x,y,zA.

xRy and yRx implies x=yxRy and yRx implies x=y

here told R is partial order on set A,

Let S be the transitive closure of the symmetric closure of the reflexive closure of R.

     You have to show three things:

A relation R is ...	if ...
reflexive	xRx
transitive	xRy and yRz implies xRz
antisymmetric
symmetrix	xRy implies yRx