Understanding of cardinality it ERD models

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I have huge trouble with understanding the cardinality.

Let's say that there Doctor and he can perform heart surgery on just one patient. Surely there are many doctors and many patients, but should the model be just like this?

PACIENT-|----------|- DOCTOR   meaning 1:1?

Does it not need to reflect that there are many doctors and many patients? Or this describes relationship between two actual instances?

Another example: Hospital runs an experiment and can have many patients in drug trials. Each trial tests just one drug and no patient can appear in more than one trial.

TRIAL |- ------<-PATIENT (MANY TO ONE - more patients in trials are allowed)

PATIENT|------|-DRUG (1:1 if one patient can only take one drug)?

But how to indicate that the same patient cannot appear in any other trial? Or is it implicit by the relations between Trial and Patient where there is 1 at the side of Trial?

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