# Two different definitions for a Complete Relation

Many sources show this definition for completeness of a relation $$\forall a, b \in A, a \neq b, (aRb) \text{ or } (bRa) \tag{1}$$ Others show only $$\forall a, b \in A, (aRb) \text{ or } (bRa) \tag{2}$$

My question, assuming that the first definition is correct, why does the definition of a complete relation include the $$a \neq b$$ in its definition? My doubt is that when given a relation and asked whether it is complete or not, which definition should I use (1) or (2) as given in the question. And why should I use that definition? For example- Given a relation On RxR R={(x,y)| x is not equal to y}. Is this relation complete? Now if I use definition (1), it is complete. If I use definition (2), it is not complete. So which is the right answer and why?

• My doubt in simple words is that when given a relation and asked whether it is complete or not, which definition should I use (1) or (2) as given in the question. And why should I use that definition? For example- Given a relation On RxR R={(x,y)| x is not equal to y}. Is this relation complete? Now if I use definition (1), it is complete. If I use definition (2), it is not complete. So which is the right answer and why? – DARE2ZLATAN Nov 1 '19 at 9:20