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1.Relation and Function
normal
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
$m n$
D
$(n+1)^m$
(KVPY-2009)
Solution
(a)
Set $A$ have $m$-elements,
Set $B$ have $n$-elements
$\left(a, b_1\right) \in K,\left(a, b_2\right) \in R \Rightarrow\left(b_1=b_2\right)$
By condition relation is a function.
$\therefore$ Total number of function (Relation) $=n^m$
Standard 12
Mathematics
