For = {0, 1}, let A * be the language defined recursively as follows: (1)

Question:

For ∑ = {0, 1}, let A ⊂ ∑* be the language defined recursively as follows:
(1) The symbols 0,1 are both in A - this is the base for our definition; and
(2) For each word x in A, the word 0 × 1 is also in A - this constitutes the recursive process.
(a) Find four different words - two of length 3 and two of length 5 - in A.
(b) Use the given recursive definition to show that 0001111 is in A.
(c) Explain why 00001111 is not in A.