1. Exercise 1 for strings and sets
1. What does each of the following expressions give?
(a) a (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) (c ) (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 })