bijections

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$. The number of possible va...

Let $\Sigma$ be the set of all bijections from $\{1, \ldots, 5\}$ to $\{1, \ldots, 5\}$, where id denotes the identity function, i.e. $\operatorname{id}(j)=j, \forall j$. Let $\cir...

Consider the set of all functions $$f:\left\{ {0,\,1,.....,2014} \right\} \to \left\{ {0,\,1,.....,2014} \right\}$$ such that $$f\left( {f\left( i \right)} \right) = i,\,\,\,$$ for...

(a) How many binary relations are there on a set A with n elements? (b) How many one - to - one functions are there from a set A with n elements onto itself