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Exercise 1 for strings and sets

Exercise 1 for strings and sets. 1. What does each of the following expressions give? (a) a 5 (b) |aba 7 b| (c) | | (d) x R , where x = abab (e) AB, where A = {a, b, c}, B = {aaaa, bbbb, cccc}. (f) A * BA * ,where A and B are the same sets defined in (e) above.

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Exercise 1 for strings and sets

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  1. Exercise 1 for strings and sets 1. What does each of the following expressions give? (a) a5 (b) |aba7b| (c) || (d) xR , where x = abab (e) AB, where A = {a, b, c}, B = {aaaa, bbbb, cccc}. (f) A*BA* ,where A and B are the same sets defined in (e) above. Answer: (a) aaaaa (b) 10 (c ) 0 (d) baba (e) AB = {aaaaa, abbbb, acccc, baaaa, bbbbb, bcccc, caaaa, cbbbb, ccccc} (f) A*BA* = { x | x = {a, b, c}* and x has aaaa, bbbb, or cccc as a substring} 2. For each of the following sets, which of the strings given below in (1) – (7) are its members? (a) {xyxR | x  {a, b, c}*, y  ccc } (b) {xx | x  {a, b, c}* } (c) {x | x  {a, b, c}* and x has more a’s than b’s. }  {aibj | j, i > 0 } (d) ({a, b, c}* - ({aibj | i > j > 0 }  {aibj | 0 < i < j }))  {aibj | j, i > 0 } (1) aaaabbbb (2) aaaa (3) aaaacccaaaa (4) bbbaaaa (5) abcccccba (6) aaaaab (7) abaaba Answer: (a): (3), (5) (b): (2), (7) (c): (6) (Notice that the members should be in {aibj | i > j > 0}) (d): (1) (Notice that the members should be in {aibi | i > 0 })

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