Let M$1$ and M$2$ be two DFAs each with $10$ states. We want to check if L$($M$1)=$

L$($M$2).$ For this, we try all strings of length at most $100,$ and observe that

for any such string x$,$ we either have $($i$)$ x in L$($M$1)$ and x in L$($M$2)$ or $($ii$)$

$5$

x $/$ in L$($M$1)$ and x $/$ in L$($M$2).$ Can we conclude that L$($M$1)=$ L$($M$2)?$ Either

prove the statement or give a counter$-$example