Basics of set theory- 2

Probability Level 2

Find the number of subsets of a set A A containing 6 distinct elements.

64 63 96 32 128 31 127 16

Mehul Arora by Mehul Arora , 20, India

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2 solutions

Mehul Arora
Feb 11, 2016

The number of subsets of a set A A containing n n elements is 2 n 2^n .

Simply applying the formula: Number of subsets = 64 \huge {\boxed {64}} .

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It would be better if you include the proof of the first line in the solution.

Nihar Mahajan - 5 years, 4 months ago

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Yes, I agree with you Nihar.

Venkata Karthik Bandaru - 5 years, 4 months ago
Shanthanu Rai
Feb 18, 2016

Given any subset S of A, an element x of A has two possibilities.

1.x belongs to S.

2.x does not belong to S.

Therefore, using multiplication principle, we multiply 2 six times to get the answer. 2^6=64 (The same idea can be extended to a set with n elements).

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