Question Regarding Polar Protic Solvents

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I'm currently studying for an organic chemistry exam and I came across polar protic solvents. I read that polar protic solvents have active hydrogen atoms that are involved in hydrogen bonding and that compounds with functional groups -OH, -NH2, -CO2H, and -SH are usually protic solvents. Then I went over a concept check question which asked whether H2O or H2S was a better protic solvent. The answer was that H2O was because it will form hydrogen bonds with the solute then it went on to say that only hydrogen atoms bonded to O, N, or F form hydrogen bonds with other atoms, thus what has confused me. If protic solvents are involved in hydrogen bonding and compounds with aforementioned functional groups are protic solvents then if the above statement is true how can compounds with the thiol and carboxylic acid functional groups be considered protic solvents?
 
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As I recall, it's like covalent and ionic bond character; it's not black and white, but a spectrum of grays. Hydrogen bonding happens when a highly electronegative atom has a hydrogen attached to it. Sulfur is pretty electronegative relative to most of the table, so it does hydrogen bond, just to a very small degree. The more electronegative the atom trying to bond to the hydrogen, the stronger the bond will be. So since oxygen is more electronegative than sulfur, water is a better protic solvent.

It's not that O, N, and F are the only elements to form hydrogen bonds, they're just the most likely, and their presence I imagine would prohibit any weaker hydrogen bonds from forming.

And besides, a carboxylic acid group has an -OH group on it.
 
thanks for clearing that up for me, it makes perfect sense now.