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Problem 1 Consider the set A of all strings of letters a- ● dcbac eba fe aba fa ● ● f of length 5. Here are a few elements of this set: What is the cardinality of each of the following sets? (This is another way of asking how many strings there are with the specified propery) 1. A itself, the set of all strings of letters a f of length 5. 2. B, the subset of A in which strings contain no repeated letters. 3. C, the subset of A in which every sequence starts with the three letters "bee".

Problem 1 Consider the set A of all strings of letters a- ● dcbac eba fe aba fa ● ● f of length 5. Here are a few elements of this set: What is the cardinality of each of the following sets? (This is another way of asking how many strings there are with the specified propery) 1. A itself, the set of all strings of letters a f of length 5. 2. B, the subset of A in which strings contain no repeated letters. 3. C, the subset of A in which every sequence starts with the three letters "bee".

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem 1** Consider the set \( A \) of all strings of letters \( a - f \) of length 5. Here are a few elements of this set: - dcbac - ebafe - abafa What is the cardinality of each of the following sets? (This is another way of asking how many strings there are with the specified property) 1. \( A \) itself, the set of all strings of letters \( a - f \) of length 5. 2. \( B \), the subset of \( A \) in which strings contain no repeated letters. 3. \( C \), the subset of \( A \) in which every sequence starts with the three letters “bee”. 4. \( D \), the subset of \( A \) in which every sequence either starts with “bee” or ends with “eab,” or both. 5. \( E \), the subset of \( A \) in which every sequence either starts with “bee” or ends with “cab”, or both. 6. \( F \), the subset of \( B \) (the set of strings with no repeated letters) which do not contain the substring “bad” in any position. - *Hint*: Figure out how many strings contain the substring “bad” and then subtract this number from the cardinality of \( B \).
Transcribed Image Text:**Problem 1** Consider the set \( A \) of all strings of letters \( a - f \) of length 5. Here are a few elements of this set: - dcbac - ebafe - abafa What is the cardinality of each of the following sets? (This is another way of asking how many strings there are with the specified property) 1. \( A \) itself, the set of all strings of letters \( a - f \) of length 5. 2. \( B \), the subset of \( A \) in which strings contain no repeated letters. 3. \( C \), the subset of \( A \) in which every sequence starts with the three letters “bee”. 4. \( D \), the subset of \( A \) in which every sequence either starts with “bee” or ends with “eab,” or both. 5. \( E \), the subset of \( A \) in which every sequence either starts with “bee” or ends with “cab”, or both. 6. \( F \), the subset of \( B \) (the set of strings with no repeated letters) which do not contain the substring “bad” in any position. - *Hint*: Figure out how many strings contain the substring “bad” and then subtract this number from the cardinality of \( B \).
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