- #1

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## Homework Statement

prove by induction that if A and B are finite sets, A with n elements and B with m elements, then AxB has mn elements

## Homework Equations

AxB is the Cartesian product. AxB={(a,b) such that a is an element of A and b is an element of B}

## The Attempt at a Solution

normally, proof by induction involves one variable. here it includes two. I guess I could say that mn=nm and therefore proving it for n+1 is the same thing as proving it for m+1. Then any increase in m or n after that is just the same thing. But somehow I still feel this isn't really justifiable.