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Are native speakers (of any given language, say English) with average IQs at a relatively young age (say, under 10 years old) without exposure to dictionaries, encyclopedias, formal education and other kinds of education know that in the case of, e.g., Jovian is an adjectival form of Jupiter?

Of course, this is just one example off the top of my head - there are plenty of other similar examples when one form of a word sounds radically different from another word form.

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    What you are asking is, effectively, how good young children are at acquiring irregular and suppletive morphological patterns, in the absence of explicit instruction. The realistic answer seems to be "pretty darn good, provided that the pattern in question is not rare". Jovian is a bad example, as it is a very infrequent term; however, irregular verbs/adjectives/nouns are acquired fast in the general case. See, e.g., Pinker's Words and Rules for verbs and Bobaljik's Universals of Comparative Morphology for adjectives. – Koldito Jul 27 '16 at 8:30
  • Addendum to my previous comment: jovian appears in rank 23022 of the Project Gutenberg frequency list, which amounts to 256 occurrences per billion words. You'd have to read about 30 average-length novels to have a good chance of encountering one instance of jovian. – Koldito Jul 27 '16 at 8:41
  • Unless you read science fiction. Jovian, Martian, Venerian, Lunar, Terran, and many other low-frequency Latinate terms are very common in space fiction. The Jovian moons (particularly the Galilean satellites) are locales for major stories. – jlawler Jul 27 '16 at 17:37
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"Know" has two meanings: be consciously aware, and have some account of that fact in your cognitive apparatus. And then, "things like that" really needs another thing like that plus a third thing that is not like that. I'll supply some examples for you – "boil" and "bullion" (also like), and "dog" / "dogs" (not the same kind of thing).

The word "Jupiter" might be known to a reasonable number of under-10 children, clearly not a majority, and all would be educated. Probably only a handful know "Jovian". So virtually none of the set you're interested in know that relationship. Likewise with "boil" and "bullion", where "boil" is probably known to most English speaking children between ages 4 and 10 (but not "bullion"). Virtually all children know "dog" and "dogs", and connect them instantly.

Very few children would understand the technical terms, so you can't ask if Jovian is the adjectival form of Jupiter or probably even if "dogs" is the plural of "dog". Most people don't talk about "adjectival forms", "plurals", so uneducated English speaking children at age 10 probably have no idea what a plural is. Even educated ones struggle, since grammar isn't taught so much.

Whether or not this is part of one's subconscious linguistic ability is hard to tell in the cases that you're interested in. There is a classical test, the wug test, that shows that children have in fact internalized regular plural formation. As far as I know, nobody has even attempted to do the same test with words like "Jovian" and "sangiovese" or "Jupiter".

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Looking at your question widely, it can be re-phrased like this:

Are native speakers with average IQs at a relatively young age without exposure to dictionaries, encyclopedias, formal education and other kinds of education know exceptions to linguistic rules?

Every language has a certain set of rules. For example, in English morphology, the regular way to build the plural number is by adding s to the noun: cat → cats.
However, there are numerous exceptions, like mouse → mice.
Ask yourself, did you learn this word as a kid? The answer would be, definitely yes.
The same would apply various noun → adjective patterns, like -'s or -ian suffixes.

However, the above depends on how common the word is. If the word is not used commonly, even a highly-educated person would have problem with its morphology. Frankly, I don't know for sure how to build a possessive/adjectival form of Jupiter in my native language; I've simply never used it in my life. :-)

Even if the word is widely used, but a certain possible form is rare, it can be a problem as well!
See Is “fish's” correct to use when referring to something that the fish owns?, for example.

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