häuslich
domestic
Relating to the house, household, or family.
Nach der Geburt des Kindes übernahm er mehr häusliche Pflichten.
After the birth of the child, he took on more domestic duties.

domestic
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domestic
Relating to the house, household, or family.
Nach der Geburt des Kindes übernahm er mehr häusliche Pflichten.
After the birth of the child, he took on more domestic duties.

The adjective 'häuslich' (domestic) is derived directly from the noun 'das Haus' (the house). The ending '-lich' turns the noun into an adjective and means 'in the manner of a house' or 'belonging to the house'.
Er ist ein sehr häuslicher Typ und liebt es, zu Hause zu kochen.
He is a very home-loving type and loves cooking at home.
There are two main uses: 'häuslich' (home-loving/domestic) can describe a person who likes being at home. But it can also describe activities or things that belong to the household.
Mein Bruder ist nicht sehr häuslich und immer unterwegs.
My brother is not very home-loving and is always out and about.
In connection with the household, 'häuslich' (domestic) is often used in fixed combinations. Common examples are 'häusliche Pflichten' (domestic duties), 'häusliche Arbeit' (housework/domestic work), or the serious term 'häusliche Gewalt' (domestic violence).
Am Wochenende erledige ich meist die häusliche Arbeit.
On the weekend, I usually do the housework.
The expression 'sich häuslich niederlassen' means to establish a permanent home. The verb here is 'sich niederlassen' (to settle down), and 'häuslich' describes the manner more precisely.
Nach vielen Umzügen wollen wir uns nun in dieser Stadt häuslich niederlassen.
After many moves, we now want to settle down in this city.
public
'öffentlich' and 'häuslich' can form a contrast between being out in society and being at home. 'öffentlich' refers to places, situations, or actions that are accessible or visible to other people. 'häuslich' relates to the house, household, or family. So 'öffentlich' fits better with streets, offices, events, or statements made in front of others; 'häuslich' fits private situations at home.

Nach dem Unfall braucht Herr Kaya für einige Wochen häusliche Pflege.
After the accident, Mr. Kaya needs home care for a few weeks.
Vor dem Termin habe ich die Adresse mit öffentlichen Verkehrsmitteln gesucht.
Before the appointment, I looked up the address using public transportation.