Breakdown of Einkabarnið á engan bróður eða systur.
bróðirinn
the brother
systirin
the sister
eiga
to own / to have (a relationship)
eða
or
Questions & Answers about Einkabarnið á engan bróður eða systur.
Why is it bróður instead of bróðir?
The verb eiga (to have, here á) requires the object to be in the accusative case. Bróðir is an irregular kinship noun, and its accusative form is bróður. In fact, its accusative, dative, and genitive singular forms are all exactly the same: bróður.
Is systur also in the accusative case here?
Yes, it is the accusative singular of systir, continuing the object of the verb á. Just like bróðir, the noun systir is irregular and changes to systur in the accusative, dative, and genitive singular.
Why does the sentence use engan instead of a feminine form, since it also applies to systur?
When a word like enginn (no/none) applies to two nouns of different genders joined by eða (or), it typically agrees with the first noun. Here, engan is the masculine accusative singular form to match bróður.
Why use á for "has" instead of hefur?
In Icelandic, the verb eiga (conjugated here as á) is used when talking about family members and close relationships. You use hafa (to have) mainly as a helping verb, or for abstract concepts and things you are temporarily holding.