Cartesian Product, Join Operations

Cartesian Product

• The cartesian product operation allows us to combine informationf rom two relations
• If a column appears in two relations, we distinguish between them by writing the name of each table as a prefix in the combined table

Example

Table Instructors

ID	name	dept_name	salary
222	Hello	Physics	165005
351	World	Chemistry	150406

Table Topics

ID	chapter_name	days_alloted	dept
20	Atomic Theory	12	Physics
13	Molecular Mixing	15	Chemistry
25	Waves and Particles	10	Physics

We can merge these tables with \(\(\quad instructors\; X \; topics\)\) To select these values, we will use \(\sigma(instructors\; X \; topics)\)

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Join

• The Join operation allows us to combine a \(\sigma\) and an \(X\) into a single operation
• \(r \, \bowtie_{\,\theta}\; s\) is the same thing as \(\sigma_\theta \;(r\; X \; s)\)

Example

The statement \(\(\quad \sigma_{\,instructors.dept\_name\,=\,topics.dept}\;(instructor\;X\; topics)\)\) is equivalent to \(\(\quad instructors\; \bowtie_{\;instructors.dept\_name\,=\,topics.dept}\;topics\)\)