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Now, we're going to talk about the Cartesian Product operator in relation to algebra.

So, the mathematical definition of it,

is that you have again two relations,

r and s. And you refer to the Cartesian Product with this symbol.

So the idea is that,

Cartesian Product what it does is that it takes every tuple in

relation r and combine it with every single tuple in

relations and the final product of the Cartesian product operator is

basically all the tuples combined together from both relations r and s. So,

let's take a look at an example.

So, let's assume you want to do a Cartesian Product between the cse courses.

So, all the courses in computer science and the cse professors.

So, you want to list all combinations of

computer science professors teaching computer science courses.

So, you want to just mix and match

the combination between professors and computer science courses.

So, the final schema is usually the schema,

it's the combination of the schema of the relation r and relation s. So, as you can see,

the output has the name and the office

which is the name of the professor and the office of the professor,

and also the other part of the schema has the course ID and the course title.

So, you combined the two schemas of

the two relations together to find for the Cartesian Product.

So, if you look at the example again,

so you have cse_profs that's

a relation that has the information about computer science professors.

We have name of professor1,

professor2 and we have the office of the professor.

And then, the other relation which is cse_courses.

It has the course ID and course title.

So, for all the computer science courses.

And the Cartesian Product of these two,

so, cse_ profs and cse_courses.

It basically combines all these tuples

from both relations together and combine the schema as well.

So, the output will be like that.

So, here you have the schema of the cse_profs,

then you have the schema of the cse_courses.

And then, these are the tuples combined altogether and to combine all of them together,

you have to find all the combinations between professor,

s and professors' tuples, and courses tuples.

So, in the professor tuples,

we have only Prof1 and Prof2.

But, to find all the combination we have to combine Prof1 with CSE412, CSE513, CSE514.

And then, do the same for Prof2.

So, this is why we have

several professor tuples that has Prof1 and several tuples that have Prof2.

So, and this is the final output of

the Cartesian Product between csc_prof and csc_courses. Thank you.