11.2 Properties of Relations

Properties of Relations

• Suppose $R$ is a relation on a set $A$.

Reflexive

• Relation $R$ is reflexive if $xRx$ for every $x\in A$. That is, $R$ is reflexive if $\forall x\in A,xRx$

Symmetric

• Relation $R$ is symmetric if $xRy$ implies $yRx$ for all $x,y\in A$. That is, $R$ is symmetric if $\forall x,y\in A,xRy\Rightarrow yRx$.

Transitive

• Relation $R$ is transitive if whenever $xRy$ and $yRz$, then also $xRz$. That is, $R$ is transitive if $\forall x,y,z\in A,((xRy)\wedge (yRz))\Rightarrow xRz$