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$)$ 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.

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