Question
Consider a Master Set S= {1,2,3,4….12} How many subsets can be formed which will contain one or more elements of S (including all S) such that the elements of the sets are integral multiples of the smallest subset of the set.
Answer: Option D
:
D
Option (d)
If 1 is the smallest element of the set, all or none of the other elements can be selected −211 different sets, as for each number from 2 to 12, there are two options, of getting selected or not getting selected. There are 11 such numbers 2-12 including both, therefore 2.2.2…..11 times = 211
Similarly, If 2 is the smallest element in the set, 4,6,8,10 and 12 can be selected in 25 ways
If 3 is the smallest element in the set 6,9,12 23 different sets
......211+25+23+22+21+6=2102
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:
D
Option (d)
If 1 is the smallest element of the set, all or none of the other elements can be selected −211 different sets, as for each number from 2 to 12, there are two options, of getting selected or not getting selected. There are 11 such numbers 2-12 including both, therefore 2.2.2…..11 times = 211
Similarly, If 2 is the smallest element in the set, 4,6,8,10 and 12 can be selected in 25 ways
If 3 is the smallest element in the set 6,9,12 23 different sets
......211+25+23+22+21+6=2102
Was this answer helpful ?
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