In the following examples we assume that the alphabet Sigma is {0, 1}. 1. 0*10*

Question

In the following examples we assume that the alphabet Sigma is {0, 1}. 1. 0*10* = {w| w has exactly a single 1}. 2. Sigma*l Sigma* = {w| w has at least one 1}. 3. Sigma*001 Sigma* = {w| w contains the string 001 as a substring}. 4. (Sigma Sigma)* = {w| w is a string of even length}.^5 5. (Sigma Sigma Sigma)* = {w| the length of w is a multiple of three}. 6. 01 union 10 = {01, 10}. 7. 0 Sigma*0 union 1 Sigma*1 union 0 union 1 = {w| w starts and ends with the same symbol}. 8. (0 union elementof)l* = 01* union 1*. The expression 0 union elementof describes the language {0. elementof}, so the concatenation operation adds either 0 or element before every string in 1*. 9. (0 union elementof)(l union elementof) = {elementof, 0, 1, 01}. 10. 1* emptyset = emptyset. Concatenating the empty set to any set yields the empty set. 11. emptyset* = {elementof}. The star operation puts together any number of strings from the language to get a string in the result. If the language is empty, the star operation can put together 0 strings, giving only the empty string.

Explanation / Answer

1) correct, 01,10,010,00100

2)correct, 01,10,010,00100,11,1111,001

3)correct ,001, 0001,1001,11001

4) correct, 00,11,0011,1100,.....

5) correct, 000,111,010,110,000000,111111,.....

6) correct,01,10

7) correct, 0,1,00,11,101,010,....

8) correct, 1,11,111,01,011

9, correct, 0,1,01

10) correct

11) correct

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