S$-$boxes is one of the process in the Data Encryption Standard $($DESprotocol$.$

Describe the function of S$-$boxes that makes DES a secure system.

i$)$

Referring to S$-$box$[1]$ in Fig. $1,$ show that S$,($x$,)$ S$,($x$2)!=$ S$($x$1$ X$2)$for x$1=000000$ and x$2=000001$