Ég kann að sýna nemandanum yddarann.

Questions & Answers about Ég kann að sýna nemandanum yddarann.

Why is nemandanum in the dative case and yddarann in the accusative?
The verb sýna (to show) is a ditransitive verb, meaning it takes two objects. Just like gefa (to give) or lána (to lend), the recipient (who you are showing something to) takes the dative case. The thing being shown takes the accusative case. Since you are showing the sharpener to the student, the recipient nemandanum is dative and the object yddarann is accusative.
Could I swap the order and say Ég kann að sýna yddarann nemandanum?
Usually, no. In Icelandic, when a verb takes a dative indirect object (the recipient) and an accusative direct object (the thing), the dative recipient almost always comes first. So it needs to follow the order of sýna + recipient (nemandanum) + thing (yddarann).
Both nemandi (student) and yddari (sharpener) are masculine words ending in '-i'. How do they get the endings '-anum' and '-ann' here?
Both are weak masculine nouns. In the singular, these nouns change their final -i to an -a in the accusative, dative, and genitive cases. So the base for both becomes nemanda and yddara. To make them 'the' student and 'the' sharpener, you add the definite article endings to that new base: -num for the dative (nemanda + num = nemandanum) and -nn for the accusative (yddara + nn = yddarann).
Why use kann here instead of veit for 'know'?
Kunna (conjugated here as kann) is used when you know how to do something, like a skill, a language, or a learned ability. Since showing the sharpener is being treated as an action you know how to perform, you use kunna að. The verb vita (to know) is strictly used for knowing facts or information.

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