4Grammar and explanations
Inviting: урих
The person you invite is the object, in the accusative; the place goes in the dative-locative. The stem of урих is урь–, with a soft sign, so: урьж байна, урьсан.
Би таныг манайд урьж байна.I you-ACC our.place-DAT invite-CONV be-PRES-FUT"I'd like to invite you to our place."
The pronouns you need are the accusatives: чамайг, таныг, тэднийг. манайд is the dative-locative of манай: "at our place, to our place".
The invitation itself: Ирээрэй!
The polite imperative –аарай of lesson 66 is the natural form for an invitation: it is warm, and it points to a future moment.
Бямба гарагт манайд ирээрэй!Saturday-DAT our.place-DAT come-IMP"Come to our place on Saturday!"
To a close friend the bare stem is fine too: Манайд ир!
Are you free? завтай, завгүй
зав is free time, so завтай is "free" and завгүй is "busy": Чи маргааш завтай юу? "Are you free tomorrow?" Answer Завтай or Завгүй. Remember that after –тай the question particle is юу.
Accepting: очно, not ирнэ
When you accept, you say очно, "I'll go there", because you will be going to your host's place: Баярлалаа, очно. Mongolian looks at the movement from where you are now. English says "I'll come"; Mongolian says "I'll go". За, тэгье! "All right, let's do that!" accepts any suggestion.
Declining politely: чадахгүй нь
Begin with Уучлаарай, use чадахгүй (can't) from lesson 64, and add нь at the end. After a verb in –хгүй, this spoken нь adds a note of regret, as if you had just realised it, and so it softens the refusal, like English "I'm afraid". Without it, Би очиж чадахгүй is a plain "I can't come", also correct but drier.
Уучлаарай, би очиж чадахгүй нь.sorry I go-CONV can-PART-NEG I'm.afraid"Sorry, I'm afraid I can't come."
Then give a short reason: Ажилтай. (I'm working.) Завгүй байна. (I'm busy.)
Another time: –ъя
A kind refusal often ends with a new plan in the "let's" form of lesson 68:
Дараа хамт цай ууя.later together tea drink-IMP"Let's have tea together another time."
Go deeper in the grammar guide: Mongolian imperatives · Politeness and address · Can, must, may: Mongolian without modal verbs