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Below is a recursive definition of a set T.
Basis:
λ ∈ T
Recursive Step: If S ∈ T, then bs ∈ T, sb ∈ T, saa ∈ T, asa ∈ T, asa ∈ T
Closure: S ∈ T only if S is A or can be obtained from A using the Recursive Step operations a finite number of times.

A. The only string of length 1 that belongs to T is .
B. Two new different elements of the set T are generated in the first execution of the recursive step.
C. All of the strings of length up to 3 inclusive, that belong to the set T, are: "", b, aa, bb, baa, aab, aaaa.
T is a set of all strings, over = {,}, containing even number of a's.


Sagot :

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