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Let, init (L) = {set of all prefixes of L},
Let L = {w | w has equal number of 0’s and 1’s}
init (L) will contain:
Let L = {w | w has equal number of 0’s and 1’s}
init (L) will contain:
- a)all binary strings with unequal number of 0’s and 1’s
- b)all binary strings with ԑ-string
- c)all binary strings with exactly one more 0's than number of 1's
- d)None of above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let, init (L) = {set of all prefixes of L},Let L = {w | w has equal nu...
Clearly init (L) = (0+1)*. Take any string in (0+1)* say 101011, we can append required number of symbols to make it a member of L like 10101100.
Most Upvoted Answer
Let, init (L) = {set of all prefixes of L},Let L = {w | w has equal nu...
Explanation:
To understand the answer to this question, let's break it down step by step.
Step 1: Find the set of all prefixes of L.
The set of all prefixes of L, denoted as init(L), is the set of all strings that can be obtained by taking a prefix of any string in L. In other words, init(L) contains all the possible initial substrings of strings in L.
Step 2: Determine the language L.
The language L is defined as the set of all binary strings where the number of 0s is equal to the number of 1s. For example, "01", "0011", "010101", etc. are all strings in L.
Step 3: Determine the content of init(L).
Since init(L) contains all the possible initial substrings of strings in L, we need to consider the possible prefixes of strings in L and determine if they belong to init(L).
Step 4: Analyze the options.
a) All binary strings with unequal number of 0s and 1s: This option does not represent the content of init(L) because it includes strings that do not fulfill the condition of having an equal number of 0s and 1s.
b) All binary strings with -string: This option is correct because init(L) contains all possible prefixes of strings in L.
c) All binary strings with exactly one more 0s than the number of 1s: This option does not represent the content of init(L) because it includes strings that do not fulfill the condition of having an equal number of 0s and 1s.
d) None of the above: This option is incorrect because option b) is the correct answer.
Therefore, the correct answer is option b) - "all binary strings with -string".
To understand the answer to this question, let's break it down step by step.
Step 1: Find the set of all prefixes of L.
The set of all prefixes of L, denoted as init(L), is the set of all strings that can be obtained by taking a prefix of any string in L. In other words, init(L) contains all the possible initial substrings of strings in L.
Step 2: Determine the language L.
The language L is defined as the set of all binary strings where the number of 0s is equal to the number of 1s. For example, "01", "0011", "010101", etc. are all strings in L.
Step 3: Determine the content of init(L).
Since init(L) contains all the possible initial substrings of strings in L, we need to consider the possible prefixes of strings in L and determine if they belong to init(L).
Step 4: Analyze the options.
a) All binary strings with unequal number of 0s and 1s: This option does not represent the content of init(L) because it includes strings that do not fulfill the condition of having an equal number of 0s and 1s.
b) All binary strings with -string: This option is correct because init(L) contains all possible prefixes of strings in L.
c) All binary strings with exactly one more 0s than the number of 1s: This option does not represent the content of init(L) because it includes strings that do not fulfill the condition of having an equal number of 0s and 1s.
d) None of the above: This option is incorrect because option b) is the correct answer.
Therefore, the correct answer is option b) - "all binary strings with -string".
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Let, init (L) = {set of all prefixes of L},Let L = {w | w has equal number of 0’s and 1’s}init (L) will contain:a)all binary strings with unequal number of 0’s and 1’sb)all binary strings with ԑ-stringc)all binary strings with exactly one more 0's than number of 1'sd)None of aboveCorrect answer is option 'B'. Can you explain this answer?
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