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Repetition of the elements are immaterial. The number of elements in a set '$A$' is denoted as $|A|$, is called the cardinality of the set, a set with no elements. Relationship between sets can be represented by venn diagrams. A relation describes certain properties of things and is a set of ordered pairs. It is a subset of ordered pairs drawn from the set of all possible ordered pairs. $R$ is a relation if. $R \subseteq {(x, y) |x\ \epsilon \ X,y\ \epsilon Y}$. Here Domain is $X$ and Codomain is $Y$.
The relational algebra uses set union, set difference, and Cartesian product from set theory, but adds additional constraints to these operators.For set union and set difference, the two relations involved must be union-compatible âthat is, the two relations must have the same set of attributes.hereas the result of a join (or inner join) consists of tuples formed by combining matching tuples in the two operands, an outer join contains those tuples and additionally some tuples formed by extending an unmatched tuple in one of the operands by fill values for each of the attributes of the other operand.