## anonymous 3 years ago 1. How many distinct binary relations can be constructed from a given set A with cardinality 3 to a given set B with cardinality 4?

1. anonymous

I think I can construct 3 * 4 + 1 distinct binary relations.

2. anonymous

I think I was lost. To know the number of binary relations I can get from to given set with known cardinalities I need to know the cardinality of the power set of the cartesian product. I know that the cardinality of a power set is given by:$\#P(A) = 2^{\#A}$

3. anonymous

And I know too that the cardinality of the Cartesian product is equal to the product of the cardinalities of every set involved. So $\#(A\times B) = \#A\cdot \#B$

4. anonymous

So $\#P(A\times B)=2^{\#A\cdot \#B}$

5. anonymous

So the number of binary relations I cant get is given by: $2^{12}$

6. anonymous

Is it right?