Question

Which of the following regular expressions denote a language comprising all possible strings of even length over the alphabet \(\{0,1\}\)?

• A. \((0+1)^*\)
• B. \((0+1)(0+1)^*\)
• C. \((00+01+10+11)^*\)
• D. \((0+1)(0+1)(0+1)^*\)

Hint:

To generate all even-length binary strings, think in pairs of symbols. The four possible pairs are \[ 00,\;01,\;10,\;11. \] Applying Kleene star to these pairs: \[ (00+01+10+11)^* \] produces every binary string whose length is \(0,2,4,6,\ldots\).

Answer 1

The Correct Option is C