The Number Of Subsets Of The Set A = {a1, a2, … an} Which Contain Even Number Of Elements Is

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The number of subsets of the set A = {a1a2, … an} which contain even number of elements is


Correct option is

For each of the first (n – 1) elements a1a2, … an – 1 we have two choices: either  lies in the subset or ai 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 an in the subset, otherwise (when odd number of elements have been added), we include it in the subset. 

Thus, the number of subsets of  which contain even number of elements is equal to .



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