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

Question

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

Smart Achievers · Accepted Answer

(2)

Ans. $2^{n} - 2$

Explanation:

Each element in A can map onto any one of the two elements of B.

Total possible functions $= 2^{n}$

Total number of surjections $= 2^{n} - 2$

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