## Question

The number of subsets of the set A = {*a*_{1}, *a*_{2}, … *a _{n}*} which contain even number of elements is

### Solution

For each of the first (*n* – 1) elements *a*_{1}, *a*_{2}, … *a _{n}*

_{ – 1}we have two choices: either lies in the subset or

*a*doesn’t lie in the subset. For the last element we have just one choice. If even number of elements have already been taken, we do not include

_{i}*a*in the subset, otherwise (when odd number of elements have been added), we include it in the subset.

_{n}Thus, the number of subsets of which contain even number of elements is equal to .

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