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In a sentence
Nemusíš mi ďakovať.
You don't need to thank me.
Nemusíš mi ďakovať, pretože si zaslúžiš len to najlepšie.
You do not need to thank me because you deserve all the best.
Nie, ďakujem.
No, thank you.
Ďakujem za informáciu.
Thanks for the information.
Examples from Tatoeba (CC BY 2.0 FR).
Source
Slovak National Corpus (SNK) ↗English gloss from the frequency publish path. Example sentences from Tatoeba (CC BY 2.0 FR).
Full attribution on References.