In mathematical relations such as reflex, symmetric, transetive and so on. Does it need to occur once or must it apply to all values?

Question

I want to know if different scenarios in relations must satisfy all the value in the relation.

In mathematical relations, a given set relation is reflexive if all the elements in the set exhibit (a,a). What about the rest of the relations? Such as symmetric, transitive, anti-symmetric and so on. Does is need to occur once, or does it need to be valid for any given values in a relation?

Answer 1

Hi Ahmed,

 

I just saw this post. Sorry it took so long.

 

There answer is that the relation must be true for any two elements in the set.

 

I hope this is helpful.

 

Best regards!