Fjallið er hátt og bókasafnið er undir því.

Breakdown of Fjallið er hátt og bókasafnið er undir því.

vera
to be
og
and
undir
under
bókasafnið
the library
fjallið
the mountain
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Questions & Answers about Fjallið er hátt og bókasafnið er undir því.

Why does fjallið end with -ið?

fjallið is the definite form of the neuter noun fjall (“mountain”). In Icelandic you don’t use a separate word for “the” – you add a suffix to the noun. For neuter nouns that suffix is -ið, so:
• fjall → fjallið = “the mountain”

Why is the adjective hátt and not something like háttur or hár?

Icelandic adjectives agree in gender, number and case with the noun they describe. The base (dictionary) form is masculine nominative (hár), but here it describes a neuter noun (fjall) and is used predicatively after er. Predicative adjectives take the nominative case, and for neuter singular that means adding -t:
• hár (masc) → hátt (neut. sing. nom.)

Why is there an -s- in bókasafnið?

bókasafnið is a compound noun made from bók (“book”) + safn (“collection” or “repository”). Icelandic often inserts a linking -s- (a genitive element) between the parts:
• bók + safn → bókasafn
Then you add -ið to make it definite:
• bókasafn → bókasafnið = “the library”

What case does undir take in this sentence?
undir can govern either accusative (motion toward) or dative (static location). Here it expresses location (“under”), so it takes the dative case.
Why is it undir því instead of undir það?
það is the neuter pronoun “it/that.” After a dative-governing preposition like undir, you must use the dative form því. This því refers back to fjallið.
Could I say bókasafnið er undir fjallinu instead of undir því?

Yes. fjallinu is the dative of fjallið, so
• bókasafnið er undir fjallinu
is equally correct. Using því simply replaces the full noun to avoid repetition.

What is the basic word order in these clauses?

Icelandic generally uses Subject-Verb-Predicate (for predicative sentences). Here each clause is:
Fjallið (Subject) er (Verb) hátt (Predicate)
Bókasafnið (Subject) er (Verb) undir því (Adverbial phrase)
They are joined by the conjunction og (“and”).

How would you say the same thing in the plural?

You change both nouns to plural definite, switch er to eru, adjust the adjective and pronoun to plural dative:
• fjöllin (the mountains) eru há (are tall)
• bókasöfnin (the libraries) eru undir þeim (are under them)
Full sentence: Fjöllin eru há og bókasöfnin eru undir þeim.