"He has shoes on."

Translation: Tá bróga air.

[jytou]

Can someone explain the "air" part? I can guess is "ar" but don't really get it.

[Knocksedan]

ar is "on"

orm (from ar mé) - on me
ort (from ar tú) - on you
air - on him
uirthi - on her
orainn - on us
oraibh - on you (plural)
orthu - on them

[jytou]

Got it, I still have quite a lot to get through... thanks!

[KSBMcCann]

If Tá + ar = "must", then what is "must" about "He has shoes on"?

[deactivated user]

Do you understand the difference between the meanings of the word "has" in
"Paul has a hat to wear"
"Paul has to wear a hat"
"Paul has a hat on"?

tá (subject) ar (object) and tá ar (subject) (verbal noun) are different grammatical structures, and they mean different things, just as "Paul has a hat to wear" and "Paul has to wear a hat" are different grammatical structures that mean different things, and neither of them are related to "Paul has a hat on".

[KSBMcCann]

When I see a sentence with tá + ag together, I look for how "have" fits into an English translation, and on Duolingo "have" invariably appears. I have assumed (oh, dear, not assumed) that if tá + ar are in a sentence together, that "must" fits into a translation somehow. So you're saying that's not necessarily so? Any hints for how a learner can differentiate?

[deactivated user]

If you can tell the difference between a noun and a verb, you can tell the difference between tá (subject) ar (object) and tá ar (subject) (verbal noun).

While tá + ag is used to indicate possession in Irish, that's not the only meaning that you can take from tá and ag - the most basic meaning of tá fear ag an doras is "there's a man at the door".

Tá an bus ag an stáisiún - "The bus is at the station"
https://forum.duolingo.com/comment/12075348

Bhíomar ag bialann inné - "We were at a restaurant yesterday"
https://forum.duolingo.com/comment/33599366

In almost all cases the difference between "X is at Y" and "Y has X" is obvious (as obvious as the difference between the "has" in "Paul has a hat to wear" and "Paul has to wear a hat"), but in certain sentences either structure could apply
Tá airgead ag an mbanc - "The bank has money" or "There is money at the bank"
https://forum.duolingo.com/comment/4481143

And obviously, if you can tell the different between a noun and a verb, you won't have any problem with:
Tá tú ag snámh - "You are swimming"
https://forum.duolingo.com/comment/4330432

[KSBMcCann]

Go raibh maith agat. I appreciate your time and your reply and links were helpful.