Final answer:
A regular expression that matches strings over the alphabet {a, b} whose length is not a multiple of 3 is (a|b)*(aa|ab|ba|bb)|(a|b), capturing strings of lengths 1 and 2, and any string followed by one or two characters.
Step-by-step explanation:
To write a regular expression that denotes the language of all strings over the alphabet {a, b} whose length is not a multiple of 3, we can construct a regular expression that matches strings of lengths 1 and 2, and then any string followed by additional segments of one or two characters.
A regular expression that matches a string of length 1 would be (a|b), and one that matches a string of length 2 would be (aa|ab|ba|bb). To denote any string (including the empty string) we use (a|b)*.
Combining these, our overall regular expression would be (a|b)*(aa|ab|ba|bb)|(a|b), which matches either any string followed by an 'a' or 'b' or any string followed by two of 'a' or 'b' in any combination, ensuring the total length is not a multiple of 3.