Question: Let A and B be sets with partitions P 1 = {A1,...,An} and P 2 = {B1,...,Bm}, respectively. Prove that P={AiBj | 1in, 1jm} is

Let A and B be sets with partitions P1 = {A1,...,An} and P2 = {B1,...,Bm}, respectively. Prove that P={Ai×Bj | 1≤i≤n, 1≤j≤m} is a partition of the set given by A×B. This is true intuitively, but i don't know how to prove it formally. How should i approach it?

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