Functions Question 708
Question: The number of surjection from $ A={1,2,…,n},n\ge 2ontoB={a,b} $ is
Options:
A) $ ^{n}P_2 $
B) $ 2^{n}-2 $
C) $ 2^{n}-1 $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] we know that, if X and Y are any two finite sets having m and n elements respectively, where $ 1\le n\le m, $ then the number of onto functions from X to Y is given by $ \sum\limits_{r=1}^{n}{{{(-1)}^{n-r}}^{n}C_{r}r^{m}\cdot r=1} $ Thus, the number of subjective mappings is $ \sum\limits_{r=1}^{2}{{{(-1)}^{2-r}}C_{r}r^{n}=( 2^{n}-2 )} $
BETA
