Test the following binary relations on the given sets S for reflexivity, symmetry, antisymmetry, and transitivity. a$.$ S$=$set of all finite$-$length strings of characters x r y $4$ number of characters in x$=$number of characters in y b$.$ S$=50,1,2,3,4,56$ x r y $4$ x$+$y$=5$ c$.$ S$=`(51,2,3,4,5,6,7,8,96)$ A r B $40$A$0=0$B$0$ d$.$ S$=`(51,2,3,4,5,6,7,8,96)$ A r B $40$A$00$B$0$ e$.$ S$=$N$$N $($x$1,$ y$1)$ r $($x$2,$ y$2)4$ x$1$x$2$ and y$1$y$2$