Your FDs are in boldface.
- Patient_ID, Theatre_ID---> Surgery_Date
Based on the sample data, I'd have to say this one is wrong. The following FDs seem to be correct for these three attributes. They're derived mainly from your assumptions, which I've pointed out in comments probably don't hold in the real world.
- Patient_ID -> {Theatre_ID, Surgery_Date}
- Surgery_Date -> Theatre_ID
- Surgery_Record_ID---> Patient_ID
Each row gets a different value for Surgery_Record_ID, so Surgery_Record_ID determines every attribute.
- surgery_Record_ID -> {patient_ID, surgery_ID, theatre_ID, Surgery_Date}
- Patient_ID---> Surgery_ID, Surgery_Record_ID, Theatre_ID
Since patients can't revisit, and since patients can have only one surgery, Patient_ID will be globally unique, just like Surgery_Record_ID. Patient_ID will determine every attribute.
- patient_ID -> {surgery_Record_ID, surgery_ID, theatre_ID, Surgery_Date}
- Patient_ID, Surgery_ID--->Theatre_ID
I covered Patient_ID above. Surgery_ID doesnt' determine anything.
Surgery_Record_ID, Patient_ID, Surgery_ID, Theatre_ID---> Surgery_Date
Surgery_Record_ID -> {Patient_ID, Surgery_Date}
- Patient_ID -> {Surgery_Record_ID, Surgery_Date}
- Surgery_Date -> {Surgery_Record_ID, Patient_ID}
Your assumptions require Surgery_Date to be unique. So Surgery_Date determines every attribute.
- Surgery_Date -> {patient_ID, surgery_ID, theatre_ID, surgery_Record_ID}