1.

Let `A={1,2,..., n}`and `B={a , b`}. Then number of subjections from `A`into `B`isnP2 (b) `2^n-2`(c) `2^n-1`(d) nC2A. ` ""^(n)P_(2)`B. `2^(n)-2`C. `2^(n)-1`D. None of these

Answer» Correct Answer - D
Given that, A = { 1, 2, 3, …, n} and B = {a, b}.
We know that, if A and B are two non-empty finite sets containing m and n elements respectively, then the number of surjection from A into B is
`""^(n)C_(m)xxm!, if n ge m`
0, if `n lt m`
Here, m = 2
` :. ` Number of surjection from A into B is
`""^(n)C_(2)xx2! =(n!)/(2!(n-2)!)xx2!`
` " " =(n(n-1)(n-2)!)/(2xx1(n-2))xx2! =n^(2)-n`


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