Suppose A = \{0, 1\} . Which of the following statements is NOT true?

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Suppose A = \{0, 1\}. Which of the following statements is NOT true?

For any k > 0, the set A^k contains twice as many strings as the set A^{k-1}.

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A^* is an infinite set.

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The set A^1 is a distinctly different set from A.

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For any k > 0, the set A^k contains the k-digit binary representations of all numbers from 0 to 2^{k-1}.

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