Which of the following regular expressions describes the language over...
A) with at least 2 consecutive 1's, any no of 0's and any no of 1's
B) exactly two consecutive 1's
C)exactly two 1's but need not be consecutive
D) any no of 1's and 0's with at least two 1's
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Which of the following regular expressions describes the language over...
Answer:
The regular expression that describes the language over {0, 1} consisting of strings that contain exactly two 1s is option 'c' - 0*10*10*.
To understand why option 'c' is the correct answer, let's break down the regular expression and analyze it step by step:
0*: This part of the regular expression matches any number (including zero) of 0s at the beginning of the string.
10*: This part matches a single 1 followed by any number (including zero) of 0s.
10*: This part matches a second occurrence of a single 1 followed by any number (including zero) of 0s.
Combining these three parts together, we can see that the regular expression matches strings that start with any number of 0s, followed by a single 1, followed by any number of 0s, followed by a second occurrence of a single 1, and finally followed by any number of 0s.
Let's analyze how this regular expression matches strings with exactly two 1s:
- 0110: The regular expression matches this string as it starts with 0s, followed by a 1, followed by 0s, followed by a second occurrence of a 1, and ends with 0s.
- 0011: The regular expression also matches this string as it starts with 0s, followed by a 1, followed by 0s, followed by a second occurrence of a 1, and ends with 0s.
On the other hand, the other options do not correctly describe the language:
- Option 'a' matches strings with at least two 1s, but it also matches strings with more than two 1s.
- Option 'b' matches strings with at most two 1s, but it also matches strings with fewer than two 1s.
- Option 'd' matches strings with at least two 1s, but it does not ensure that there are no more than two 1s.
Therefore, option 'c' is the correct regular expression that describes the language over {0, 1} consisting of strings that contain exactly two 1s.
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