Discrete Math for Computer Science, unit: Relations. Core concepts, terminology, and worked-example cues a college student meets for this unit, building on prior units without repeating them. Front: a term, concept, or short problem cue. Back: the definition, explanation, or answer.
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- What is a relation, in discrete mathematics?
- A set of ordered pairs describing a connection between elements of two sets
- What is a binary relation?
- A relation between elements of exactly two sets (or one set with itself)
- What is a reflexive relation?
- A relation where every element is related to itself
- What is a symmetric relation?
- A relation where if a is related to b, then b is also related to a
- What is a transitive relation?
- A relation where if a relates to b and b relates to c, then a relates to c
- What is an antisymmetric relation?
- A relation where if a relates to b and b relates to a, then a must equal b
- What is an equivalence relation?
- A relation that is reflexive, symmetric, and transitive
- What is an equivalence class?
- The set of all elements related to a given element under an equivalence relation
- What is a partial order?
- A relation that is reflexive, antisymmetric, and transitive
- What is a total order?
- A partial order where every pair of elements is comparable
- What is the composition of two relations?
- A new relation formed by chaining pairs from the first relation to pairs in the second
- What is the inverse of a relation?
- A relation formed by reversing the order of every ordered pair in the original relation
- What is a Hasse diagram used for?
- Visually representing a partial order, omitting reflexive and transitive edges for clarity
- What is a relation's representation as a matrix called?
- A relation matrix, indicating with 1s and 0s which pairs are related
- What does it mean for a relation to be a function?
- Each element of the domain is related to exactly one element of the range
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