Question

The number of relations $R$ from an m -element set $A$ to an $n$-element set B satisfying the condition $\left(a\,b_{1}\right)\in R , \left(a, b_{2}\right)\in R \Rightarrow b_{1}=b_{2 }$ for $a\in A ,b_{1},b_{2}\,\in B$ is

• A. $n^{m}$
• B. $2^{m+n}-2^{m}-2^{n}$
• C. $mn$
• D. $(n+1)^{m}$

Answer 1

Answer: (A)

Set $A$ have $m$-elements,
Set $B$ have $n$-elements
$\left(a\,b_{1}\right)\in R , \left(a, b_{2}\right)\in R $
$\Rightarrow \left(b_{1}=b_{2}\right)$
By condition relation is a function
$\therefore $ Total number of function (Relation) $=n^{m}$