Does a composite primary key break the first normal form

From a set of FDs, you can only infer a set of candidate keys.

A "primary key" is one particular member of that set of candidate keys that you elect to be "primary". And there are no scientific rules that tell you which one you should choose - you can pick just any key and label it "primary".

In your first example, you should end up with a set of candidate keys

{ {T G} {G X} }

In the second example, you should end up with a singleton set of candidate keys

{ {X Y} }

As for how to arrive at the set of keys, you can take a look at https://stackoverflow.com/questions/5735592/determine-keys-from-functional-dependencies/5736174#5736174

Short version:

CREATE TABLE Relation
( stu_id INT NOT NULL REFERENCES Student,
  par_id INT NOT NULL REFERENCES Parent,
  PRIMARY KEY (stu_id, par_id)
) ;

Long version:

• Why use short forms for names, like stu_id and par_id? Why not student_id? Saving typing 3-4 characters? How will you differentiate between parent_id and parameter_id? Or school_id and schoolmaster_id?

• The name "Relation" is not very descriptive for a relationship. (Note also that in relational model terminology, "relation" has a meaning very close to "table".) I couldn't come with a good name though, so we could use "Guardian" or "Student_Parent" (this combination is often used in intersection tables)

• The short version above is just an example. While it is working, it uses a lot of shortcuts, like the inline references. It's far better in my opinion, to name all constraints and declare all (primary, unique, foreign key and check) constraints after the column declarations, like in the long version below.

• It's also good to choose some naming conventions anduse them consistently in all the tables, e.g. Tablename_PK for the primary keys, ReferencedTable_referencingTable_FK for the foreign keys, Something_UQ for the unique constraints, etc.

CREATE TABLE Guardian
(                                        -- columns
  student_id INT NOT NULL, 
  parent_id INT NOT NULL,
                                         -- constraints
  CONSTRAINT Guardian_PK                 -- the name of the PK constraint
    PRIMARY KEY (student_id, parent_id),

  CONSTRAINT Student_Guardian_FK         -- the name of the FK constraint
    FOREIGN KEY (student_id) 
    REFERENCES Student (student_id)
      ON UPDATE CASCADE                  -- the actions of the FK
      ON DELETE RESTRICT,
  CONSTRAINT Parent_Guardian_FK          -- second FK
    FOREIGN KEY (parent_id) 
    REFERENCES Parent (parent_id)
      ON UPDATE CASCADE
      ON DELETE RESTRICT
) ;