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InterviewSolution
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If A is a finite set with m elements then prove that the number of subsets is`2^m` |
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Answer» Let `A` contains `1` element such that `A = {1}`. Then, subsets of `A = {},{1} `. `:.` Number of subsets of `A = 2 =2^1.` Let `A` contains `2` elements such that `A = {1,2}`. Then, subsets of `A = {},{1},{2},{1,2}. ` `:.` Number of subsets of `A = 4 =2^2.` Let `A` contains `3` elements such that `A = {1,2,3}`. Then, subsets of `A = {},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}. ` `:.` Number of subsets of `A = 8 =2^3.` Similarly, for `A` having `m` elements, number of proper subsets will be `2^m`. |
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