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If $R$ is a relation in Relational Data Model and $A_1,A_2,\dots A_n$ are the attributes of relation $R$, what is the cardinality of $R$ expressed in terms of domain of attributes?

1. $\mid R\mid\leq\mid \text{ dom }(A_1) \times \text{ dom }(A_2)\dots \text{ dom }(A_n)\mid$
2. $\mid R\mid\geq\mid \text{ dom }​​​​​​​(A_1)\times \text{ dom }​​​​​​​(A_2)\dots \text{ dom }​​​​​​​(A_n)\mid$
3. $\mid R \mid = \text{ max } ( \mid \text{dom}(A_1 ) \mid, \mid \text{ dom }(A_2) \mid , \dots \mid \text{ dom } (A_n) \mid)$
4. $\mid R \mid = \text{ min } ( \mid \text{dom}(A_1 ) \mid, \mid \text{ dom }(A_2) \mid , \dots \mid \text{ dom } (A_n) \mid)$​​​​​​​

Option A

the term cardinality refers to the uniqueness of data values contained in a particular column (attribute) of a database table. The lower the cardinality, the more duplicated elements in a column.

In the context of databases, cardinality refers to the uniqueness of data values contained in a column.
Cardinality refers to a number. It gives the number of unique values that appear in the table for a particular column.

cardinality of relation= multipication of domain of each attribute

$∣R∣≤∣ dom (A1)× dom (A2)… dom ​​​​​​​(An)∣$

For eg: you have a table called Person with column Gender. Gender column can have values either 'Male' or 'Female".

Then the cardinality of Gender column is 2, since there are only two unique values that could possibly appear in that column – Male and Female.

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