Let $A = \{a, b, c\}$ and $R = \{(a, c), (b, b), (c, a)\}$ be a relation on $A$.
Determine whether $R$ is reflexive, symmetric, transitive and anti-symmetric, or not.
Let $A = \{a, b, c\}$ and $R = \{(a, c), (b, b), (c, a)\}$ be a relation on $A$.
Determine whether $R$ is reflexive, symmetric, transitive and anti-symmetric, or not.
Let $A = \{a, b, c\}$ and $R = \{(a, c), (b, b), (c, a)\}$ be a relation on $A$.
Reflexive?
We need to have that for all $x \in A$, $(x, x) \in R$.
Symmetric?
We need to have that for all $x, y \in A$, if $(x, y) \in A$ then $(y,x)\in A$.
Transitive?
We need to have that for all $x, y, z \in A$, if $(x, y)$ and $(y, z)$ are in $R$, then $(x, z)$ is in $R$.
Antisymmetric?
We need to have that for all $x, y \in A$, if $(x, y), (y, x) \in R$, then $x = y$.