Question

To determine whether the given relation \(R\) has any primary key.

Short answer

The given relation \(R\) has no primary key.

Step-by-step solution

Given data

The relation \(R\) defined by the ordered pairs:

\(\{ (0,a),(0,b),(1,a)(2,b)\} \) ……(1)

Concept of Relation

The relation between the two sets is defined as the collection of the ordered pair, in which the ordered pair is formed by the object from each set.

Example:\(\left\{ {\left( { - {\bf{2}},{\rm{ }}{\bf{1}}} \right),{\rm{ }}\left( {{\bf{4}},{\rm{ }}{\bf{3}}} \right),{\rm{ }}\left( {{\bf{7}},{\rm{ }} - {\bf{3}}} \right)} \right\}\),usually written in set notation form with curly brackets.

Calculation to check whether the given relation has any primary key

In\(R\), the element (the first coordinate\(0\)) is related to two different elements\(a\)and\(b\)and the element (the second coordinate\(a\)is related to two different elements\(0\)and\(1\).

So no domain is a primary key.

Hence, there is no primary key for the relation \(R\).