Translation:Lukas is a man and Anna is a woman.
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Ein/Eine" can mean both "a/an" and "one".
Ein Mann= A man/One man.
Eine Frau= A woman/One woman.
No. The English sentence uses the indefinite article "a", so in German you also should use the indefinite article "ein/eine".
NB: "Mann" is a masculine noun, so you would use "der" if you used the definite article.
They are both different conjugations of the verb "sein" (to be). If you are using the browser version of Duolingo, the conjugation of this verb is given in the Tips and notes section of the lesson page. If you are using the app, this section is not available. So, here's the rundown. Of course, "to be" is a very irregular verb.
1st person - ich bin (I am)
2nd person - du bist (you-informal are)
3rd person - er/sie/es ist (he/she/it is)
1st person - wir sind (we are)
2nd person - ihr seit (you-plural are)
3rd person - sie sind (they are)
- Sie sind (you-formal are)