Difference between Reflexive and Symmetric in Discrete Maths?
This is what I understand:
Reflexive -> <a,a=a>, <b,b=b> uses = to describe.
Symmetric -> <a,b>, <b,a> uses ≤, ≥, = to describe.
Transitive -> <a,b>, <b,c>, <a,c> uses <, >, = to describe.
But why is this is a symmetric <1,1>, <2,2>, <3,3>, <4,4>, <5,5>?
2 Answers
$\begingroup$A relation is reflexive if, for all $a$, $a$ is "related" to $a$ ($aRa$ is true).
A relation is symmetric if, whenever $aRb,$ then $bRa$ (so $\le$ is not symmetric because if $a\le b$ it does not follow that $b\le a$, but equality is symmetric).
A relation is transitive if, given $aRb$ and $bRc$, then $aRc$. e.g. if $a|b$ and $b|c$ then $a|c$ so divisibility is transitive.
$\endgroup$ 5 $\begingroup$Symmetric means that for every $(a,b)\in R$ also $(b,a)\in R$
$(c,c)$ is symetric with itself.
(Reflexive means that such $(c,c)$ exists at all, and does not necessarily mean that the relation is symmetric)
$\endgroup$
