Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Discrete mathematics, probability and continuous mathematics / 3 / d

R

A

A \times A

. Its properties are quantified over elements of

A

A reflexive relation satisfies $\forall a \in A, a R a$ .
A symmetric relation satisfies $\forall a, b \in A, a R b \Rightarrow b R a$ .
An antisymmetric relation satisfies $\forall a, b \in A, (a R b \land b R a) \Rightarrow a = b$ .
A transitive relation satisfies $\forall a, b, c \in A, (a R b \land b R c) \Rightarrow a R c$ .
An irreflexive relation satisfies $\forall a \in A, \neg (a R a)$ .
A serial relation satisfies $\forall a \in A \exists b \in A, a R b$ .