How to store array values?
Student table:

id | name


In this table you will have the students.



Sickness table:

id | name


In this table will have the sicknesses. It will have a row for all the sicknesses (cancer, diabetes, and so on).



Relative table:

id | name


This table will have the relations: "mom", "dad", "brother" and so on.



The trick what you need is a bridge table, or associative entity.

These are used to map many-to-many relations. And.. much more.

Because in this case, you need more than a single many-to-many relation. In fact, you need a "many-to-many-to-many relation". Essentially, it is an associative entity between 3 entities.

It is uncommon, but possible and can be handled pretty well in the DB design.

So, you need to have also a fourth table, with the following columns:

student_id | relative_id | sickness_id


If the table has a row, for example, (3, 4, 5), it would mean that the relative with id 4 of student with id 3, had the sickness with id 5.

On this way, you don't need multiple tables for the different sicknesses, it would be a very bad design.

(student_id, relative_id, sickness_id) should be a primary key of this bridge table. The induvidual columns will be also foreign keys to the corresponding student, relative or sickness tables.