41. Because a preorder is a binary relation , the symbol d " can be used as the notational device for the relation. 42. A derived binary relation between two sets is the subset relation, also called "'set inclusion " '. 43. Unlike most structures in order theory, a cyclic order is not modeled as a binary relation , such as " ". 44. They belong to the class of binary relations but they have three additional properties : reflexivity, anti-symmetry and transitivity. 45. If is a critical pair, then the binary relation obtained from by adding the single relationship is also a partial order. 46. Recall that a preorder on " X " is a binary relation on " X " which is transitive. 47. Binary relations are used in many branches of mathematics to model concepts like " function is defined as a special kind of binary relation.48. Binary relations are used in many branches of mathematics to model concepts like " function is defined as a special kind of binary relation . 49. In some fields, it is common to use infix notation for binary relations and functions, instead of the prefix notation defined above. 50. Formally, ZFC is a signature has equality and a single primitive binary relation , set membership, which is usually denoted ".
