Proving the Equality of Finite Cartesian/Cross Products for Sets A and B

[kmikias]

Homework Statement

show for finite sets A,B,that m(A x B ) = m(A)m(B).

Homework Equations

I don't see relevant equation but we can treat to like cartesian/cross product.

The Attempt at a Solution

I tried to think it as (x,y) for m(A x B ) . if we let A = { 1,2} and B= {3,4} then those product will be {1,3},{2,4},{1,4},{1,4} isn't it? but then i am confused with m(A)m(B) because it seems like multiplication .

I need some hint to prove this statement/question.
thank you.

 

[Dick]

m(A)m(B) is multiplication. In your example you listed the elements of the cross product. But you got it wrong. AxB={{1,3},{1,4},{2,3},{2,4}}. There are 4 elements in there. So m(AxB)=4. m(A)=2 and m(B)=2. So m(A)m(B)=2*2=4. So m(AxB)=m(A)m(B).