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Unformatted text preview: w âˆˆ A * where A is an alphabet. The reversal of w , denoted w R , is defined recursively based on  w : 1. If  w  = 0, i.e., if w = Î» (the empty string), then w R = Î» R = Î» ; 2. If  w  > 0, let w = ua where u âˆˆ A * and a âˆˆ A (i.e., a is the last symbol and u is the prefix), then define w R = ( ua ) R = au R . Based on this recursive definition, prove that for any two strings x , y âˆˆ A *, ( xy ) R = y R x R . (Hint: Use induction on  y  â‰¥ 0.) 4) Let T, W, and X be sets of strings over the alphabet L = {a,b}. Prove or disprove the following statement: if (T âˆ© W)* = (T âˆ© X)* then W = X. 5) Let T and W be sets of strings over the alphabet L = {a,b}. Prove or disprove the following statement: if T âŠ† W, then (WT)* âŠ† W*...
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This document was uploaded on 07/14/2011.
 Spring '09

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