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Question
Mark the correct alternative in the following question:
Let A = {1, 2, ... , n} and B = {a, b}. Then the number of subjections from A into B is
Options
nP2
2n - 2
2n - 1
nC2
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Solution
As, the number of surjections from A to B is equal to the number of functions from A to B minus the number of functions from A to B whose images are proper subsets of B.
And, the number of functions from a set with n number of elements into a set with m number of elements = mn
So, the number of subjections from A into B where A = {1, 2, ... , n} and B = {a, b} is 2n - 2 (As, two functions can be many-one into functions)
Hence, the correct alternative is option (b).
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