A function f: X → Y is bijective, where X and Y are finite sets. The number of possible relations from X to Y is 512. If X and Y have exactly one element in common, then what is the number of elements in X ∪ Y?

Question

anonymous · Answer

What does being a bijection tell you about the cardinality of X and Y? Can they have a different number of elements and still have a bijection between them?
 
A relation is basically a set of ordered pairs. How many ordered pairs can you make based on the cardinalilty of X and Y? 

Each of the ordered pairs is either part of the relation or not part of the relation. If the number of possible ordered pairs is n, then the number or possible relations is 2^n. There are two choices for each ordered pair. What must n be to have 512 possible relations?