rec0719_key - COT3100 Summer2001 Recitation on Languages...

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COT3100 Summer’2001 Recitation on Languages and Machines 07/19/2001 1. Let A , B and C be sets of strings. Prove or disprove that A ( B - C ) = A B - A C . Only one subset relation can be proved, namely we can prove that A B - A C A ( B - C ). It actually means that A B - A C is “smaller” then A ( B - C ), because there might be a string that belongs to both A B and A C , although it can not be represented as some prefix from A and a suffix that belong to both B and C. So, here is a counterexample that disproves A ( B - C ) A B - A C . A ={ a , ab }, B ={ b }, C ={ λ }. B - C ={ b }, A ( B - C )={ ab , abb }, A B ={ ab , abb }, A C ={ a , ab }, and A B - A C = { abb }. So, ab A ( B - C ), but ab A B - A C , so it’s not the case, that always A ( B - C ) A B - A C . 2. Let A , B and C be sets of strings. Prove or disprove that if A B , then A * B * . Assume
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rec0719_key - COT3100 Summer2001 Recitation on Languages...

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