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Consider the Following regular expressions
r1 = 1(0 + 1)*
r2 = 1(1 + 0)+
r3 = 11*0
r2 = 1(1 + 0)+
r3 = 11*0
Q. What is the relation between the languages generated by the regular expressions above ?
- a)L (r1) ⊆ L (r2) and L(r1) ⊆ L(r3)
- b)L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)
- c)L (r1) ⊇ L (r2) and L(r2) ⊆ L(r3)
- d)L (r1) ⊇ L (r3) and L(r2) ⊆ L(r1)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the Following regular expressionsr1 = 1(0 + 1)*r2 = 1(1 + 0)+...
Clearly r1 is a superset of both r2 and r3 as string 1 can not be generated by r2 and r3. r2 is a superset of r3 as string 11 is not present in L(r3) but in L(r2).
Most Upvoted Answer
Consider the Following regular expressionsr1 = 1(0 + 1)*r2 = 1(1 + 0)+...
Explanation:
To understand the relation between the languages generated by the regular expressions r1, r2, and r3, let's analyze each regular expression individually.
r1 = 1(0 1)*
This regular expression generates strings starting with 1, followed by zero or more occurrences of either 0 or 1. The language generated by r1 can be represented as L(r1) = {1, 10, 11, 100, 101, 110, 111, ...}.
r2 = 1(1 0)
This regular expression generates strings starting with 1, followed by either 1 or 0. The language generated by r2 can be represented as L(r2) = {11, 10}.
r3 = 11*0
This regular expression generates strings starting with 1, followed by one or more occurrences of 1, and ending with 0. The language generated by r3 can be represented as L(r3) = {10, 110, 1110, 11110, ...}.
Relation between the languages:
Now, let's analyze the relation between the languages generated by these regular expressions.
L(r1) L(r2)
The language L(r1) contains all strings starting with 1, followed by zero or more occurrences of either 0 or 1. The language L(r2) contains all strings starting with 1, followed by either 1 or 0. Therefore, the intersection of L(r1) and L(r2) is the set of strings starting with 1, followed by either 0 or 1. This can be represented as L(r1) L(r2) = {10, 11, 100, 101, 110, 111, ...}.
L(r2) L(r3)
The language L(r2) contains all strings starting with 1, followed by either 1 or 0. The language L(r3) contains all strings starting with 1, followed by one or more occurrences of 1, and ending with 0. Therefore, the intersection of L(r2) and L(r3) is the set of strings starting with 1, followed by either 1 or 0, and ending with 0. This can be represented as L(r2) L(r3) = {10}.
Therefore, the correct answer is option B: L(r1) L(r2) and L(r2) L(r3).
To understand the relation between the languages generated by the regular expressions r1, r2, and r3, let's analyze each regular expression individually.
r1 = 1(0 1)*
This regular expression generates strings starting with 1, followed by zero or more occurrences of either 0 or 1. The language generated by r1 can be represented as L(r1) = {1, 10, 11, 100, 101, 110, 111, ...}.
r2 = 1(1 0)
This regular expression generates strings starting with 1, followed by either 1 or 0. The language generated by r2 can be represented as L(r2) = {11, 10}.
r3 = 11*0
This regular expression generates strings starting with 1, followed by one or more occurrences of 1, and ending with 0. The language generated by r3 can be represented as L(r3) = {10, 110, 1110, 11110, ...}.
Relation between the languages:
Now, let's analyze the relation between the languages generated by these regular expressions.
L(r1) L(r2)
The language L(r1) contains all strings starting with 1, followed by zero or more occurrences of either 0 or 1. The language L(r2) contains all strings starting with 1, followed by either 1 or 0. Therefore, the intersection of L(r1) and L(r2) is the set of strings starting with 1, followed by either 0 or 1. This can be represented as L(r1) L(r2) = {10, 11, 100, 101, 110, 111, ...}.
L(r2) L(r3)
The language L(r2) contains all strings starting with 1, followed by either 1 or 0. The language L(r3) contains all strings starting with 1, followed by one or more occurrences of 1, and ending with 0. Therefore, the intersection of L(r2) and L(r3) is the set of strings starting with 1, followed by either 1 or 0, and ending with 0. This can be represented as L(r2) L(r3) = {10}.
Therefore, the correct answer is option B: L(r1) L(r2) and L(r2) L(r3).
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Community Answer
Consider the Following regular expressionsr1 = 1(0 + 1)*r2 = 1(1 + 0)+...
From my point of view d option is correct
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Consider the Following regular expressionsr1 = 1(0 + 1)*r2 = 1(1 + 0)+r3 = 11*0Q. What is the relation between the languages generated by the regular expressions above ?a)L (r1) ⊆ L (r2) and L(r1) ⊆ L(r3)b)L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)c)L (r1) ⊇ L (r2) and L(r2) ⊆ L(r3)d)L (r1) ⊇ L (r3) and L(r2) ⊆ L(r1)Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the Following regular expressionsr1 = 1(0 + 1)*r2 = 1(1 + 0)+r3 = 11*0Q. What is the relation between the languages generated by the regular expressions above ?a)L (r1) ⊆ L (r2) and L(r1) ⊆ L(r3)b)L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)c)L (r1) ⊇ L (r2) and L(r2) ⊆ L(r3)d)L (r1) ⊇ L (r3) and L(r2) ⊆ L(r1)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the Following regular expressionsr1 = 1(0 + 1)*r2 = 1(1 + 0)+r3 = 11*0Q. What is the relation between the languages generated by the regular expressions above ?a)L (r1) ⊆ L (r2) and L(r1) ⊆ L(r3)b)L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)c)L (r1) ⊇ L (r2) and L(r2) ⊆ L(r3)d)L (r1) ⊇ L (r3) and L(r2) ⊆ L(r1)Correct answer is option 'B'. Can you explain this answer?.
Consider the Following regular expressionsr1 = 1(0 + 1)*r2 = 1(1 + 0)+r3 = 11*0Q. What is the relation between the languages generated by the regular expressions above ?a)L (r1) ⊆ L (r2) and L(r1) ⊆ L(r3)b)L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)c)L (r1) ⊇ L (r2) and L(r2) ⊆ L(r3)d)L (r1) ⊇ L (r3) and L(r2) ⊆ L(r1)Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the Following regular expressionsr1 = 1(0 + 1)*r2 = 1(1 + 0)+r3 = 11*0Q. What is the relation between the languages generated by the regular expressions above ?a)L (r1) ⊆ L (r2) and L(r1) ⊆ L(r3)b)L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)c)L (r1) ⊇ L (r2) and L(r2) ⊆ L(r3)d)L (r1) ⊇ L (r3) and L(r2) ⊆ L(r1)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the Following regular expressionsr1 = 1(0 + 1)*r2 = 1(1 + 0)+r3 = 11*0Q. What is the relation between the languages generated by the regular expressions above ?a)L (r1) ⊆ L (r2) and L(r1) ⊆ L(r3)b)L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)c)L (r1) ⊇ L (r2) and L(r2) ⊆ L(r3)d)L (r1) ⊇ L (r3) and L(r2) ⊆ L(r1)Correct answer is option 'B'. Can you explain this answer?.
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ample number of questions to practice Consider the Following regular expressionsr1 = 1(0 + 1)*r2 = 1(1 + 0)+r3 = 11*0Q. What is the relation between the languages generated by the regular expressions above ?a)L (r1) ⊆ L (r2) and L(r1) ⊆ L(r3)b)L (r1) ⊇ L (r2) and L(r2) ⊇ L(r3)c)L (r1) ⊇ L (r2) and L(r2) ⊆ L(r3)d)L (r1) ⊇ L (r3) and L(r2) ⊆ L(r1)Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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