Question: 5. Write a legal regular expression for the following regular language. L = { w | w (0 + 1)* and w begins and ends

5. Write a legal regular expression for the following regular language.

L = { w | w (0 + 1)* and w begins and ends with either 00 OR 11}.

For example the strings 00, 00011011011, 111, and 110000100 are all in the language L.

6. Write a legal regular expression for the following regular language.

L = { w | w (0 + 1)* and w contains an even number of 1s AND an even number of 0s}.

Thus 010101, 00011101, 0011, 11 etc. are all elements of L.

7. Give a lambda-NFA for the following regular expression.

(0+1)*00

8. Give a lambda-NFA for the following regular expression.

0+1+00+(01)*

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