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Let $w \in \sum$$*$ be a string, with $\sum$ being the alphabet. Let $w^R$ be the reversal of string $w$, using induction prove that $(w^R)(w^R). . .(\text{for k times}) = (ww . . .(\text{for k times}))^R.$
asked in Set Theory & Algebra by Veteran (58k points) | 84 views
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For length 1 string w = a

(aR)(aR)...(for k times)=(aa...(for k times))R

For length 2 string w = ab

(abR)(abR)...(for k times)=(abab...(for k times))R

babababababab..ba = babababababa..ba

so for string for length k  

(wR)(wR)...(for k times)=(ww...(for k times))R

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@debashish..can you pls give any good links to see such proofs for discrete maths questions?

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