The Number Of Surjections From A = {1, 2,...n},onto B = {a, B} Is

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Question

easy

Correct option is

2ⁿ – 2

where A has n elements and B has 2 elements .

Each elements of A can go to 2 elements of B. Hence there will be 2. 2. 2….n times = 2ⁿmappings.

But if each elements of A either goes to a only of B or goes to b only of B then in these two cases the mapping will not be surjective.

Hence the number of surjective mappings is 2ⁿ– 2.