Kennslubókin útskýrir þessa reglu með mörgum góðum dæmum.

Kennslubókin is a compound word plus a suffixed article:

• kennsla = teaching, instruction
  → kennslu- is the genitive/combining form used in compounds
• bók = book
• -in = the (definite article, feminine singular)

So:

• kennslu + bók → kennslubók = textbook (literally teaching-book)
• kennslubók + in → kennslubókin = the textbook

Icelandic usually forms things like textbook as a single compound rather than two separate words like kennslu bók.

Kennslubókin is:

• nominative (subject case)
• singular
• feminine
• definite (has -in, meaning the)

The verb útskýrir (explains) needs a subject in the nominative case. So we use the nominative definite form:

• nominative indefinite: kennslubók = a textbook
• nominative definite: kennslubókin = the textbook

Forms like kennslubókar would be other cases (e.g. genitive), which are not correct for the subject here.

Útskýra is the infinitive form: to explain.
In the sentence we need the present tense, 3rd person singular, to match kennslubókin (the textbook):

Conjugation (present tense, singular):

• ég útskýri = I explain
• þú útskýrir = you (sg.) explain
• hann / hún / það útskýrir = he / she / it explains

Kennslubókin is like hún (she; feminine singular), so we must use útskýrir:

• Kennslubókin útskýrir … = The textbook explains …

Because þessa reglu is in the accusative case, used for the direct object of the verb.

• The verb útskýrir takes a direct object in the accusative:
  • útskýrir hvað? → þessa reglu (explains what? this rule)

Forms:

• regla (feminine noun = rule)

  • nominative: regla (used as subject)
  • accusative: reglu (used as direct object)

• þessi (this) – feminine singular:

  • nominative: þessi
  • accusative: þessa

They have to agree:

• nominative: þessi regla = this rule (as subject)
• accusative: þessa reglu = this rule (as object)

Here the rule is the thing being explained, so we need accusative: þessa reglu.

Important singular and plural forms:

Singular:

• nominative: regla (a rule – subject)
• accusative: reglu (a rule – object)
• dative: reglu
• genitive: reglu

Plural:

• nominative: reglur
• accusative: reglur
• dative: reglum
• genitive: reglna or reglna/regla (you may see variation; reglna is common)

In the sentence, we need accusative singular, so we use reglu: þessa reglu.

The preposition með can take either accusative or dative, depending on the meaning.

• When með means with, by means of, using, it takes the dative case.
• Here it means: explains this rule *with / by means of many good examples* → dative.

So the whole phrase mörgum góðum dæmum is in dative plural:

• dæmi (example), neuter:
  • nom/acc plural: dæmi
  • dative plural: dæmum

Adjectives and quantifiers have to agree in case, number, and gender:

• margur (many), neuter dative plural: mörgum
• góður (good), neuter dative plural: góðum
• dæmi, neuter dative plural: dæmum

So we get: með mörgum góðum dæmum.

In Icelandic, adjectives and quantifiers agree with the noun in:

• case (here: dative)
• number (here: plural)
• gender (here: neuter)

So:

• dæmi is neuter, plural, dative → dæmum
• margur must match: neuter, plural, dative → mörgum
• góður must match: neuter, plural, dative → góðum

You cannot leave mörg góð dæmi (that would be nominative/accusative); the preposition með forces everything in the phrase to dative: mörgum góðum dæmum.

No, not in this sentence.

• með here requires the dative case, so the correct forms are:
  • mörgum (dative plural)
  • góðum (dative plural)
  • dæmum (dative plural)

Mörg góð dæmi would be nominative or accusative plural, which would clash with með in this meaning. So:

• ✔ með mörgum góðum dæmum
• ✘ með mörg góð dæmi (wrong case here)

Icelandic usually shows definiteness by adding an article ending to the noun, rather than a separate word:

• bók = book
• bókin = the book

With the compound:

• kennslubók = textbook
• kennslubókin = the textbook

For þessa reglu, we are using þessi (this) as a demonstrative, not just a plain definite article. So:

• reglan = the rule (definite article ending)
• þessi regla / þessa reglu = this rule (demonstrative, declined for case)

In the sentence, the speaker wants to point to a specific rule, so þessa reglu (this rule) is more precise than just regluna (the rule).

This is the most natural, neutral word order:

• Subject: Kennslubókin
• Verb: útskýrir
• Object: þessa reglu
• Adverbial phrase: með mörgum góðum dæmum

Icelandic allows some flexibility, especially for emphasis, but you must keep the verb in second position in main clauses.

Examples (all grammatical, but with different emphasis):

• Kennslubókin útskýrir þessa reglu með mörgum góðum dæmum.
  – neutral, most common.

• Kennslubókin útskýrir með mörgum góðum dæmum þessa reglu.
  – extra emphasis towards þessa reglu at the end.

Starting with the adverbial is also possible, but then the verb still has to be second:

• Með mörgum góðum dæmum útskýrir kennslubókin þessa reglu.
  – emphasises with many good examples.

All of these are acceptable; they just sound slightly different in focus.

If we wanted with a good example (singular), we would make the whole phrase singular, still in the dative:

• dæmi (example), neuter singular:
  • nom/acc: dæmi
  • dative: dæmi (same form)
• margur (many) would no longer be used; we might use einum (one) or just drop the number.
• góður (good), neuter dative singular: góðu

Examples:

• með einu góðu dæmi = with one good example
• með góðu dæmi = with a good example

So the full sentence could be:

• Kennslubókin útskýrir þessa reglu með einu góðu dæmi.
• Kennslubókin útskýrir þessa reglu með góðu dæmi.

Dæmi (example) is a neuter noun with a regular plural pattern:

• Singular:

  • nom/acc: dæmi
  • dat: dæmi
  • gen: dæmis

• Plural:

  • nom/acc: dæmi
  • dat: dæmum
  • gen: dæma

So dæmum is the dative plural form, used here because of með:

• með dæmum = with examples (in the sense: by means of examples)
  → then we add mörgum and góðum to make með mörgum góðum dæmum.