Question

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?

Answer 1

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

Answer 2

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:\[\#P(A) = 2^{\#A}\]

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

Is it right?