How many subsets of {1, 2, 3 ... 11} contain at least one even integer? ?->(Show Answer!)

1. How many subsets of {1, 2, 3 ... 11} contain at least one even integer?

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By: anil on 05 May 2019 02.40 am

Total number of subsets that can be formed with the left of 11 elements = $$2^{11}$$ = 2048
The number of subsets which contain only odd numbers(1, 3, 5, 7, 9, 11} = $$2^{6}$$ = 64
Number of subsets which contain at least one even integer = Total number of subsets - the number of subsets which contain only odd numbers
$$Rightarrow$$ 2048 - 64 = 1984. Hence, option C is the correct answer.

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MCQ-> I want to stress this personal helplessness we are all stricken with in the face of a system that has passed beyond our knowledge and control. To bring it nearer home, I propose that we switch off from the big things like empires and their wars to more familiar little things. Take pins for example! I do not know why it is that I so seldom use a pin when my wife cannot get on without boxes of them at hand; but it is so; and I will therefore take pins as being for some reason specially important to women.There was a time when pinmakers would buy the material; shape it; make the head and the point; ornament it; and take it to the market, and sell it and the making required skill in several operations. They not only knew how the thing was done from beginning to end, but could do it all by themselves. But they could not afford to sell you a paper of pins for the farthing. 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