What is the grammatically correct way to express these words in writing?
My foremost source, The Associated Press Stylebook, prefers pre-existing with a hyphen, explaining:
In general, AP considers it appropriate to use a hyphen when the prefix ends in a vowel and the word that follows begins with the same vowel:
pre-exist and pre-empt but pregame and prenatal
Webster’s New World College Dictionary (Fifth Edition), AP’s recommended alternate source, suggests:
preexist: a verb meaning to exist previously.
pre-existence or preexistence when used as a noun or an adjective
Although the tendency now is to drop the hyphen with most words that have prefixes, my research indicates otherwise in the case of pre-existing. Each of these online sources sticks with the hyphenated version, and it is by no means a complete list:
oxforddictionaries.com | wgntv.com | redstate.com | Fox59.com | adn.com | reddit.com | cscmediagroupus.com | thefederalist.com | nytimes.com | wsj.com (Wall Street Journal) | LATimes.com (Los Angeles Times) | chicagotribune.com
Merriam-webster.com considers preexist an appropriate verb and preexisting an appropriate adjective, and others such as dictionary.com and wiktionary.org say either the hyphenated or non-hyphenated version is correct.
The Publication Manual of the American Psychological Association lists preexperimental with no hyphen, but an online APA Research Style Crib Sheet developed by Professor Russ Dewey of Georgia Southern University directs, “Do not hyphenate common prefixes (posttest, prewar, multiphase, nonsignificant) unless needed for clarity (pre-existing).”
When it comes to health care, The Associated Press Stylebook treats it as two words in all cases, considering it a noun phrase:
Who provides your health care?
What kind of health care coverage do you have?
Please examine a number of health care plans before you decide.
Note that health care should not be hyphenated when used as a compound modifier — health care coverage, health care plan, health care facility — but in examples such as these, a hyphen is appropriate:
He had a number of health care-related questions.
Her health care coverage-based fears were resolved.
The AP guide says to use health care as one word only if it is an organization’s official name — American College of Healthcare Executives — or is the name of an award such as Top 25 Women in Healthcare.
Yet the guide’s recommended second reference, Webster’s New World College Dictionary, considers healthcare correct is all cases.
The American Psychological Association also prefers health care.
My view: Decide how you prefer to express pre-existing / preexisting and health care / healthcare, and respect your readers by being consistent in your usage of each.
And don’t count on spellcheck to guide you in these cases.
For insights about other words with prefixes that do or don’t need hyphens, see the list in appendix of my book: Grammar For People Who Hate Rules (pp. 135–136)
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