How to structure the database to avoid duplicates in a table

I am doing this exercise where I have to build an sql database (MySql) to store information on private lessons offered by teachers. These are the rules:

• There is just one predifined week with slot times from Monday to Friday (15-19)
• Each teacher can teach 1 or more courses
• Each course can be teached by multiple teachers
• One user can book just one lesson in a selected hour
• One teacher can book just one lesson in a selected hour

This is how I implemented it:

USER(Name, Surname, Email (PK), Password)
TEACHER(Name, Surname, Email (PK), Password) 
COURSE(Title (PK))
SLOTTIME(Day (PK), Hour (PK))

TEACHES(EmailTeacher, TitleCourse) all attributes are PK, FK(EmailTeacher -> Teacher, TitleCourse -> Course)
BOOKING(EmailUser, EmailTeacher, TitleCourse, Day, Hour) all attributes are PK, FK((EmailUser -> User), 
(EmailTeacher, TitleCourse -> Teaches), (Day, Hour -> SlotTime))

This solution causes me two problems, or at least they are the ones I identified:

1. I can have the same User booked with different Teacher and different Course at the same day and hour
2. I can have the same User booked with the same Teacher at the same day and hour but with different Course

Here is an example:

BOOKING('[e-mail]', '[e-mail]', 'Database I', 'Monday', 16) // FIRST INSERT
BOOKING('[e-mail]', '[e-mail]', 'Algorithms', 'Monday', 16) // DIFFERENT TEACHER AND COURSE
BOOKING('[e-mail]', '[e-mail]', 'Database II', 'Monday', 16) // SAME TEACHER AND DIFFERENT COURSE

What I want to obtain is a table where the rules indicated above are respected, but I can’t figure out how to implement it.

Answer

Sort-out the logical design first, then go into details.

-- Teacher TCH exists.
--
teacher {TCH}
     PK {TCH}

-- Course CRS exists.
--
course {CRS}
    PK {CRS}

-- Time slot TIM exists.
--
slot {TIM}
  PK {TIM}

-- Teacher TCH teaches course CRS.
--
teacher_course {TCH, CRS}
            PK {TCH, CRS}

FK1 {TCH} REFERENCES teacher {TCH}
FK2 {CRS} REFERENCES course  {CRS}

-- Teacher TCH booked time slot TIM for course CRS.
--
teacher_slot_course {TCH, TIM, CRS}
                 PK {TCH, TIM}
                 SK {TCH, TIM, CRS}

FK1 {TCH, CRS} REFERENCES teacher_course {TCH, CRS}

FK2 {TIM} REFERENCES slot {TIM}

-- Student (user) USR exists.
--
user {USR}
  PK {USR}

-- Student USR signed-up for course CRS.
--
user_course {USR, CRS}
         PK {USR, CRS}

FK1 {USR} REFERENCES user    {USR}
FK2 {CRS} REFERENCES course  {CRS}

-- Student USR booked time slot TIM
-- for course CRS with teacher TCH.
--
user_slot_course_teacher {USR, TIM, CRS, TCH}
                      PK {USR, TIM}

        FK1 {USR, CRS} REFERENCES
user_course {USR, CRS}

                FK2 {TCH, TIM, CRS} REFERENCES
teacher_slot_course {TCH, TIM, CRS}

Note:

All attributes (columns) NOT NULL

PK = Primary Key
AK = Alternate Key   (Unique)
SK = Proper Superkey (Unique)
FK = Foreign Key