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