Question

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

• A. $2^{100} - 2$
• B. $2^{100}$
• C. $2^{99} - 2$
• D. $2^{99}$

Answer 1

Answer: (A)

$2^{100} - 2$

Answer 2

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 $2^{100} - 2$.