Write regular expressions for the following languages. By $$word$,$ we mean

an alphabetic string separated from other words by whitespace, any relevant

punctuation, line breaks, and so forth.

$1.$ the set of all strings with two consecutive repeated words $($e$.$g$.,$Humbert Humbert$$ and $$the the$$ but not $$the bug$$ or $$the big bug$)$;

$2.$ all strings that start at the beginning of the line with an integer and that

end at the end of the line with a word;

$3.$ all strings that have both the word grotto and the word raven in them

$($but not, e$.$g$.,$ words like grottos that merely contain the word grotto$)$;

$4.$ write a pattern that places the first word of an English sentence in a

register. Deal with punctuation.