Mathematical Proofs: Cartesian Product
The Cartesian Product is an operation between two sets A and B. The output of the operation is a set consisting of all ordered pairs (a,b) where "a" is from A and "b" is from B. The videos below work several proofs involving Cartesian products.
Cartesian Product Example 01
Running Time: 7:20
We work with two indexed families of sets Ai, and Bi. Define Cij as the Cartesian product of Ai and Bj, we show that union Cij is equal to the Cartesian product of union Ai with union Bj.
Cartesian Product Example 02
Running Time: 5:49
This problem works with the sets A, B, and C and shows that two different sets (involving Cartesian products and set differences) are equal to each other.