If a relation is reflexive is it symmetric and transitive ?
let ~ means " in relation with "
if A is a set , ~ is a relation on $A$, prove that:
if $a$~$a$ for any $a$ $\in$ A then
1- $x$~$y$ $\rightarrow$ $y$~$x$
2- $x$ ~$y$ , $y$ ~ $z$ $\rightarrow$ x~z
if this is wrong , give an example to a reflexive relation which is not transitive or symmetric