I noticed that there are words "dissoluble", "dissolute", and "soluble", "solute". In one word, the terms with "dis-" and without "dis-". What is the difference between them?
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Dissoluble means soluble? What a country.
They do mean the same thing, except that dissoluble is not in common use whereas soluble is. I would suggest that in scientific and academic circles you use the term soluble to claim that something can be dissolved. In a more casual setting, dissoluble would be alright.
A second note is that "soluble", if you don't specify, usually means "water soluble." I'm not sure if this same assumption exists for dissoluble.
Actually, there is a difference.
Soluble means specifically a substance being dissolved, typically in a liquid:
Whereas dissoluble that something can be dissolved, period:
and is typically used in a legal sense, such as an "easily dissoluble union".
Thus if you are talking about a substance, such as sugar, you would use soluble. If you are talking about a more abstract concept, such as a legal union, you would use dissoluble.
There is also apparently another definition of "soluble", which is something that is solvable:
This is not a usage I have ever seen as an American English speaker, and a google ngram implies it is no longer in heavy use. It seems to have been more popular in British English, so it may be that soluble is still used in BrE in everyday conversations.