I'm confused why there is a red underline when I shorten certain words.
Words which are OK:
I've, You've, We've
Words which have a red underline, meaning they're wrong:
Should've, Will've, Shall've
Why are the above words wrong?
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This may reflect your spell/grammar software's inadequacies—it may not recognize these contractions. See our Canonical Post on this subject.
However, if you actually typed these words with initial capitals, it is possible that the software is correct. There is no reason to capitalize these words in the middle of a sentence, and none of these constructions ordinarily appears at the beginning of a formal written sentence. In Standard English only the first auxiliary in a verb group is inverted with the subject: we write Should I have done it? rather than Should have I done it?, and so forth. Even in conversation you rarely hear Shoulda X with a pronoun X, only with fairly "heavy" subjects like or “Shoulda General Eisenhower relieved Patton?” or “Shoulda the Poplar Street Bridge been closed?” Those are colloquial constructions which few grammar checkers are likely to be able to distinguish.
It's hard to say what the "rules" are for what contractions are legal. People rarely say "should've", etc, and almost never write them, because they are awkward to pronounce.
Most contractions eliminate a syllable. "Can not" is two syllables, "can't" is one, so you've made your language a little more concise. But "should have" is two syllables, and "should've" ends up being pronounced "should-uv" or sometimes "should-ah", which is still two syllables, so you've saved nothing. (You sometimes see less educated people write "should of" to represent such a contraction.) Well, I suppose it's a little "smoother" to say "should-ah" then "should have", less change in position of the jaw, but the gain is small.