Question

How many subsets contain the set A={n,t,r}
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Answer 1

Answer:

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Answer 2

Answer:

2^4 = 16. The empty set, {A}, {B}, {C}, {D}, {A, B}, {A, C}, {A, D}, }B, C}, {B, D}, {C, D}, {A, B, C}, {A, B, D}, {A,C, D}, {B, C, D}, and {A, B, C, D} itself.

Generally, to construct a subset, list all elements of the set and to each element assign either YES (belongs to the subset) or NO (does not belong to the subset). This can be done in 2 ways for each element; therefore, if the original set has n elements, the total number of possible choices is 2*2*2*…*2 (n times), i.e. 2^n.