Mathematically, a relation on a set X is a subset of
X ×X. In GAP a relation on X is a general mapping
from X to itself. In fact, the category IsBinaryRelation is
the same as the category IsEndoGeneralMapping.
Of course, a binary relation can have the properties:
IsReflexiveBinaryRelation, IsTransitiveBinaryRelation and
IsSymmetricBinaryRelation. When all three are true, we call
the relation an equivalence relation.
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GAP 4 manual