One-to-One Cardinality

One to One Cardinality has two possible cases where we have the case of either total participation or no participation at one end.

There are two possibilities

Total Participation at One End

For example, consider the below ER diagram. 

A1 and B1 are the primary keys of E1 and E2 respectively. In the above diagram, we have total participation at the E1 ends. Only a single table is required in this case having the primary key of E2 as its primary key. Since E2 is in partial participation, atleast one entry in E2 does not participate in relationship set, but all entries in E1 are related to an entry in E2. Therefore E2 cannot be null for any value of E1, but E1 will be null for atleast one value of E2.

Refer Case-1 at https://www.w3wiki.org/mapping-from-er-model-to-relational-model

Note: Only 1 table is required.

No Participation at One End

A1 and B1 are the primary keys of E1 and E2 respectively. 

The primary key of R can be A1 or B1, but we can’t still combine all three tables into one. if we do so, some entries in the combined table may have NULL entries. So the idea of merging all three tables into one is not good. But we can merge R into E1 or E2. So a minimum of 2 tables is required.

Below are the Gate Previous Year Questions.
https://www.w3wiki.org/gate-gate-cs-2008-question-82/ 
https://www.w3wiki.org/gate-gate-cs-2008-question-83/  

Pre-Requisite: ER Diagram

Entity-Relationship (ER) Diagram is a diagrammatic representation of data in databases, it shows how data is related to one another. In this article, we require previous knowledge of ER diagrams and how to draw ER diagrams.

Minimization of ER Diagram simply means reducing the quantity of the tables in the ER Diagram. When there are so many tables present in the ER DIagram, it decreases the readability and understandability of the ER Diagram, and it also becomes difficult for the admin also to understand these. Minimizing the ER Diagram helps in better understanding. We reduce tables depending on the cardinality.