ABC(doc-firstname, doc-surname, doc-gender, doc-rego, doc-qualification, pat-ID, pat-givename, pat-surname, pat-gender, pat-DOB, pat-addr, pat-phone, app-ID, app-datetime, app-type)
● A doctor has a unique registration number (doc-rego) and is also described by name, gender and qualification.
● A patient is identified by a unique patient ID (pat-ID) and has other information.
● Each appointment by a patient with a doctor is assigned a unique appointment ID (app-ID). An appointment can be of the long or short type.
Would these Functional dependencies work for this relation?
fd1: doc-rego -> doc-firstname, doc-surname
fd2: patID -> pat-givename, pat-surname, pat-gender, pat-DOB, pat-addr, pat-phone
fd3: app-ID -> app-datetime, app-type
In fd1 you should add doc-qualification (asssuming that each doctor has a unique qualification).
Then, note the phrase “Each appointment by a patient with a doctor is assigned ...” implies that an appointment concerns a unique doctor and a unique patient. In other words, the app-ID, in addition to the attributes app-datetime, app-time determines also a doctor (so doc-rego) and a patient (so pat-ID), so you should modify fd3 in this way:
fd3: app-ID -> app-datatime, app-time, doc-rego, pat-ID