1. Let L, L2 and L3 be languages over some alphabet . In each part below,...

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1. Let L, L2 and L3 be languages over some alphabet . In each part below, state the relationship between the given two languages. Are they equal, is one a subset of the other, do they have an empty or non-empty intersection? Give reasons (proof!) for your answers, and counter- examples where needed. (a) L (L ~ L3) versus L L2 0 L L3. (b) LnL versus (L ^ L)*. (c) LL versus (L L2)*. (d) L (LL)* versus (LL2)* L. 1. Let L, L2 and L3 be languages over some alphabet . In each part below, state the relationship between the given two languages. Are they equal, is one a subset of the other, do they have an empty or non-empty intersection? Give reasons (proof!) for your answers, and counter- examples where needed. (a) L (L ~ L3) versus L L2 0 L L3. (b) LnL versus (L ^ L)*. (c) LL versus (L L2)*. (d) L (LL)* versus (LL2)* L.