About this interrogative phrase

Ar is the interrogative form of the copula in the conditional mood and past tense. It translates, broadly, as did…? and would…?. It lenites, when followed by a lenitable consonant.

Maith is an adjective, meaning good.

Leat is a prepositional pronoun, meaning with you.

Thus, ar mhaith leat [whatever]? means would you like [whatever]? (Literally, 'would [whatever] be good with you?'.)

Notes

The copula, is, is one of the two verbs to be in Irish, the other being bí. They experss different kinds of being though. Briefly, is is used to refer to essential, permanent qualities ('he is a man') and bí is used to refer to transient ones ('he is tired').

Very often in Irish, statements and questions regarding feelings toward things ('I love fish', 'she doesn't like dancing', 'do they respect him?'…) are expressed using a construction based on the copula. This construction is made up of:

• The copula itself.
• An appropriate adjective.
• The prepositional pronoun formed from the preposition le, meaning with, to or for.
• Or sometimes the prepositional pronoun formed from the preposition ar, meaning on.

Note the underlying structure of the following phrases:

• Is maith liom X: I like X (literally, 'X is good with me').
• Is maith leat X: You like X (literally, 'X is good with you').
• Is gráin liom X: I loath X (literally, 'X is abhorrent with me').
• Is gráin leat X: You loath X (literally, 'X is abhorrent with you').
• Nach breá leo X?: Don't they love X? (literally, 'isn't X fine with them?').
• Nach breá léi X?: Doesn't she love X? (literally, 'isn't X fine with her?').
• Ba lag liom X: I wouldn't think much of X (literally, 'X would be weak with me').
• Ba leasc liom X: I'd be reluctant to X (literally, 'X would be lazy with me').
• Is beag orm X: I don't think much of X (literally, 'X is small on me').

Prepositional pronouns formed from the preposition le

• liom: with me.
• leat: with you.
• leis: with him; with it (masculine).
• léi: with her; with it (feminine).
• linn: with us.
• libh: with ye (plural).
• leo: with them.

The same prepositional pronouns' emphatic forms

• liom-sa: with me.
• leat-sa: with you.
• leis-sean: with him; with it (masculine).
• léi-se: with her; with it (feminine).
• linn-ne: with us.
• libh-se: with ye (plural).
• leo-san: with them.