Test the following relations on the given sets S for the properties reflexivity, symmetry, anti$-$

symmetry, and transitivity. For each property that doesn$$t hold, give a specific reason why.

$($a$)$ S $=\{2,1,0,1,2\}$

xRy $|$x$|=|$y$|$

$($b$)$ S $=$ set of all finite$-$length strings of characters

xRy $$ first character of x $=$ first character of y

$($c$)$ S $=$ set of all finite$-$length strings of characters

xRy $$ number of characters in x $$ number of characters in y