Page "Equivalence relation" Paragraph 25

* The relation " is a sibling of " ( used to connote pairs of distinct people who have the same parents ) on the set of all human beings is not an equivalence relation.

Although siblinghood is symmetric ( if A is a sibling of B, then B is a sibling of A ) and transitive on any 3 distinct people ( if A is a sibling of B and C is a sibling of B, then A is a sibling of C, provided A is not C ( Note that " is a sibling of " is NOT a transitive relation, since A R B, and B R A implies A R A by transitivity )), it is not reflexive ( A cannot be a sibling of A ).

The small modification, " is a sibling of, or is the same person as ", is an equivalence relation.