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  • Let A = {1, 2, 3, ..., n} and B = {a, b}. Then the number of surjections from A to B is (a) nP2 (b) 2n – 2 (c) 2n – 1 (d) None of these

Let A = \{ 1, 2, 3, ..., n \}     and  B = \{ a, b \}  . Then the number of surjections from A to B is

(a) \textsuperscript{n}P\textsubscript{2}

(b) 2\textsuperscript{n} - 2

(c)2\textsuperscript{n} - 1

(d) None of these 
 

Answers (1)

(d)

It is given that, A = \{ 1, 2, 3, ..., n \}     and B = \{ a, b \} \\

Say, the number of elements in set A  and B are m  and n respectively.

Therefore, \textsuperscript{n}C\textsubscript{m} \times m!  is the number of surjections from A to B, for n \ngeq m \\

Given, m=2.

Therefore, the number of surjections from A to B 

= nC_2 \times 2! = n!/[2! \times (n-2)!] = n(n - 1) = n\textsuperscript{2} - n \\

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