"Das Mädchen ist willkommen."
Not really sure what this sentence means in English. "Welcome" has at least 3 meanings:
1) greeting = Willkommen 2) reply to thanks e.g. A: "The girl thanked you" B: "The girl is welcome" 3) permitting or accepting something, e.g. "The girl is welcome to take a leaflet"
In other languages a different word would be used for each sense. Given that English is quite close to German it is plausible that willkommen could be used for all senses but it just seems a bit odd, can someone else clarify?
Although I'm a bit late, I hope you will read this: Willkommen is only used in the sense of 1), not only as greeting, but also as adjective. In this manner, that you're welcome at your parents place, they would welcome you with open arms. That's 'willkommen sein' in german, being requested, demanded, desired, whatsoever.
In addation: 2) You're welcome. = Gern geschehen. (- I did that gladly). 3) In german, you would either use an adverb (like 'gern') or a modal particle (http://duolingo.com/#/comment/122572), but usually combined with a recommanding verb. For your exapmple: Sie darf sich gern eine Broschüre nehmen. Another one: 'Sie soll sich ruhig setzen'.
I was listening at my friends German yesterday when the computer brought up the word "single" and it was used with the same meaning as in English by saying: "Die Single" referred to a person. I would like you to know that is totally wrong. Referred to a person the meaning of "single" is, for a woman you would say: "Alleinstehende" and for a man: "Alleinstehender"
I don't know what this has to do with the lesson at hand, but the word 'single' referring to a single person is certainly used in Germany, I've heard it for example in ads for dating websites. In fact it's in the dictionary as a colloquialism. http://dict.tu-chemnitz.de/deutsch-englisch/Single.html