Answer
$A$ $X$ $B$={(course, professor) | course $\in$ A and professor $\in$ B}
Work Step by Step
A=Courses offered by Mathematics Department
B=Mathematics professors
By the definition of Cartesian Product:
$A$ $X$ $B$={(course, professor) | course $\in$ A and professor $\in$ B}
Example-
If the university offers only the mathematics courses Calculus and Differential Equation and if the university has only mathematics professor Ankita and Himanshu.
A={Calculus, Differential Equation}
B={Ankita, Himanshu}
$A$ $X$ $B$={(Calculus,Ankita), (Differential Equation,Ankita),(Calculus,Himanshu), (Differential Equation,Himanshu)}
This cartesian productcould be used to determine all the possible ways in which they have the mathematics professor teaching mathematics courses that the university offers.
