Answer: a.
S = {aa ab ba bb}
This clearly shows that that every string that belongs to this language has an even length including 0 length.
This language can be depicted as following
S* = {∧ aa ab ba bb aaaa aaab aaba aabb bbaa . . .}
Regular Expression for this can be
RE = (aa+ab+ba+bb)*
So S* contains all the strings of a's and b's that have even length. This means all strings of even length.
Explanation:
b.
S* contains all possible strings of a's and b's that have length divisible by 3
This means some of the possible strings examples are:
aaa, bbb, aaabbb, aaaaaa, bbbbbb and so on.
Length divisible by 3 means the length of string such as aaa is 3 which is divisible by 3, also aaaaaa has length 6 which is divisible by 3
This should be something like this:
(( a + b ) ^3)*
For example a^3 = aaa which is divisible by 3
Regular expression can be:
RE of S* = (aaa + bbb)*
For example string bbbbbbbbb has length 9 which is divisible by 3
So the language is
S* = { ∧ aaa bbb aaabbb aaaaaa aaaaaabbb...}
Explanation:
