prove mathematically that the number of subsets of a set consisting of n elements is 2^n

Asked by Chandropal Parashor | 26th Jul, 2013, 08:14: AM

Expert Answer:

Let A be any set containing n elements. Then, one of its subsets is the empty set.
Other than this,
the number of singleton subsets of A = n = nC1
the number of subsets of A, each containing 2 elements = nC2
the number of subsets of A, each containing 3 elements = nC3
... ...
the number of subsets of A, each containing n elements = nCn
Therefore, 
Total number of all possible subsets of A
= 1 + nC1 nC2 nC3 + ... + nCn
= (1 + 1)n           [Using Binomial theorem]
= 2n

Answered by  | 28th Jul, 2013, 02:44: PM

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