Consider the following two regular expressions over the alphabet {0,1}: 𝑟 =…
2024
Consider the following two regular expressions over the alphabet {0,1}:
𝑟 = 0∗ + 1∗
𝑠 = 01∗ + 10∗
The total number of strings of length less than or equal to 5, which are neither in 𝑟 nor in 𝑠, is _________
Answer: 44 — Answer: 44 Brief explanation: Total number of binary strings of length ≤ 5 = 2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 = 63. For length 0: r contains the empty…
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Correct answer: 44
Answer: 44
Brief explanation:
Total number of binary strings of length ≤ 5 = 2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 = 63.
For length 0: r contains the empty string, s contains none, so union count = 1.
For length 1: r contains "0" and "1" (both 0* and 1*), s also contains "0" and "1" (0 1* and 1 0*). The union count for length 1 = 2.
For each length n = 2,3,4,5: r contributes two strings (all-0s and all-1s) and s contributes two distinct strings (0 followed by all 1s, and 1 followed by all 0s), with no overlap, so union count per length = 4. Total for these four lengths = 16.
Total number of strings that are in r or s for lengths ≤5 = 1 + 2 + 16 = 19. Therefore number of strings of length ≤5 that are neither in r nor in s = 63 - 19 = 44.
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