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Let L be any language. Define even (W) as the strings obtained by extracting from W the letters in the even-numbered positions and even(L) = { even (W) $\mid$ W $\in$ L}. We define another language Chop (L) by removing the two leftmost symbols of every string in L given by Chop(L) = {W $\mid \mathcal{v}$ W \in L, with $\mid \mathcal{v} \mid$ =2}. If L is regular language then

1. even(L) is regular and Chop(L) is not regular
2. Both even(L) and Chop(L) are regular
3. Even(L) is not regular and Chop(L) is regular
4. Both even(L) and Chop(L) are not regular

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+1 vote

Since in both case the word obtained after removal belongs to that particular language L. and the language L is regular

so both the Languages defined by even and Chop are regular

by Active (1.9k points)