$10\mathrm{.}1$ Consider an array segment b$[$O$..$n $-1],$ where $0$::; n$.$ Let j and k be two integer variables satisfying $0$ ::; j ::; k $<$ n$.$ By b$[$j$..$k$]$ we mean the subarray of b consisting of b$[$j$],$ b$[$j $+1],...,$ b$[$k$].$ The segment b$[$j$..$k$]$ is empty if j$=$k$+$l$.$

Translate the following sentences into boolean expressions. For example, the first onecanbewrittenas $($ViIj ::;i::;k:b$[$i$]=0).$Someofthestatementsmaybe ambiguous, in which case you should write down all the reasonable possibilities. Simplify the expressions where possible. You may use abbreviations $-$e$.$g$.$ use xEb$[$O$..$n$-1]$ for $($:JiI$0$::;i