Functions Practice Questions

Suppose X and Y are sets and |X| and |Y| are their respective cardinality. It is given that there are exactly 97 functions from X to Y. From this one can conclude that

Let R denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$ . The inverse function of $f$ is given by

Let A and B be sets with cardinalities m and n respectively. The number of one-one mappings from A to B, when $m \lt n$ , is