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  4. The number of onto mappings from the set A = 1, 2, ....., 100 to set B = 1, 2 is:

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Q. The number of onto mappings from the set A = {1, 2, ....., 100} to set B = {1, 2} is:

Relations and Functions - Part 2

Solution:

The total no. of elements in A = 100. And the total no. of elements in B = 2.
Hence no. of possible onto mapping in $2^{100}$.
But this also contain the no. of elements in B differently, thus the total no. of possible onto mapping from the set A to set B is $2^{100} - 2$.