Let A={a, b, c}. Find a regular expression r such that L(r) consists of all words w where:

Each word w=x1x2xnL(r) has a property: xk=a if k=2m+1. 2.15. If wL(r) starts with ab then w ends with c. 2.16. If w=x1x2xnL(r) and xk=a then at least xk-1=a or xk+1=a. Equivalent description: if a word contains the letter a, then a is written at least twice consecutively. 2.17. Each word w=x1x2xnL(r) has a property: xk=b if k=2m. Moreover L(r) does not contain empty word. 2.18. If aw then a is followed by two consecutive bs. 2.19. If cw then c is preceded by aa. 2.20. If wL(r) then w does not contain the cc. Equivalent description: there is no word in L(r) containing cc. 2.21. Let wL(r). If bw then aw. 2.22. If wL(r) then the length l(w)=2k. Equivalent description: All words in L(r) have even length. 2.23. If wL(r) then w contains three cs and one of cs is the last letter in w. Equivalent description: each word w in L(r) contains three cs and one of cs is the last letter in w. 2.24. L(r)={wA |l(w)=2k+1}. Equivalent description: L(r) consists of all words from A having odd length. 2.25. Each word wL(r) contains at least three as. 2.26. There is no word in L(r) containing cb. Equivalent description: L(r) consists of all words w which do not contain the subword cb. 2.27. Let wL(r). If aw then w does not contain b righter than a. 2.28. Each word w=x1x2xnL(r) has a property: xk=c if k=2m. 2.29. Each word wL(r) contains at least four bs. 2.30. If wL(r) then w starts and end with the same letter.