contrast.deber-deber-de
Deber vs deber de: must (duty) vs must (guess)
Deber + infinitive = obligation (debes llegar a las ocho); deber de + infinitive = probability (debe de estar durmiendo). Speech blurs it; writing shouldn't.
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Explication
Two nearly identical structures carry opposite meanings. Deber + infinitive expresses obligation or duty: debes llegar a las ocho ('you must arrive at eight'), los socios deben firmar ('the partners must sign'). Deber de + infinitive expresses probability — an inference: debe de estar durmiendo ('he must be sleeping', i.e. he probably is).
The little de is the whole difference. Debe pagar = 'he must pay' (he's obliged); debe de ganar bien = 'he must earn well' (I infer it). The same split works in the negative: no debe hacer eso ('he shouldn't do that') versus no debe de saberlo ('he probably doesn't know it').
In real speech the de is dropped constantly, so obligation and inference often share deber + infinitive and context disambiguates. But the distinction is still the careful, correct norm — worth producing in writing and formal speech, where deber de for a guess reads as precise rather than wrong.
Exemples
Both partners must sign.
Région: global
He's not answering; he must be on the plane.
Région: global
It's already two; the bank must be closed.