| a. | [A-Za-z]+ | One or more capital or lower case letters |
| b. | [a-z]*b | Zero or more lower case letters, followed b y a b. |
| c. | .*([A-Za-z]+) \1.* | Zero or more characters, followed by one or more capital or lower case letters, followed by a space, followed by the same sequence of one or more capital or lower case letters, followed by zero or more characters. |
| d. | b+(ab+)* | One or more bs, followed optionally by an a followed by one or more bs, followed optionally by an a followed by one or more bs... |
| e. | ^[0-9].* |[^\w\n][A-Za-z]+$ | Beginning of line, a digit, zero or more characters, a space or anything that's not a letter or a number or a new line, followed by one or capital or lower case letters, end of line. |
| f. | .*\Wgrotto\W.*\Wraven\W.*|.*\Wraven\W.*\Wgrotto\W.* | Zero or more characters, a non-word character, the sequence grotto, a non-word character, zero or more characters, a non-word character, the sequence raven, a non-word character, zero or more characters... all that OR: Zero or more characters, a non-word character, the sequence raven, a non-word character, zero or more characters, a non-word character, the sequence grotto, a non-word character, zero or more characters. |
| a. | [A-Za-z][A-Za-z]* | Any capital or lower case letter, zero or more capital or lower case letters. |
| b. | [a-z]*b | Zero or more lower case letters, a b |
| c. | .*\([A-Za-z][A-Za-z]*\) \1.* | Zero or more characters, a sequence of one capital or lower case letter followed by zero or more capital or lower case letterse, then a space, then the same sequence as before again, then zero or more characters. |
| d. | bb*\(abb*\)* | a b, zero or more bs, then optionally, an a followed by a b and zero or more bs, then optionally, an a followed by a b and zero or more bs... |
| e. | ^[0-9].*[^a-zA-Z0-9\n][A-Za-z][A-Za-z]*$ | Beginning of line, any digit, zero or more characters, any character that is not a letter or number or a newline, any capital or lower case letter, zero or more capital or lower case letters, end of line. |
| f. | .*[^A-Za-z0-9]grotto[^A-Za-z0-9] .*[^A-Za-z0-9]raven[^A-Za-z0-9].*| .*[^A-Za-z0-9]raven[^A-Za-z0-9] .*[^A-Za-z0-9]grotto[^A-Za-z0-9].* |
Zero or more characters, a non-alphanumeric, the sequence grotto, another non-alphanumeric, zero or more characters, a non-alphanumeric, the sequence raven, another non-alphanumeric, zero or more characters... all that OR: Zero or more characters, a non-alphanumeric, the sequence raven, another non-alphanumeric, zero or more characters, a non-alphanumeric, the sequence grotto, another non-alphanumeric, zero or more characters. |
Note: As these are regular expressions for languages, I've included a lot of .* that you wouldn't need when using regular expressions for search in a program that returns any line containing a string matching the regular expression.