Consider the following two regular expressions over the alphabet {0,1}: 𝑟 =…

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.