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Question

If a set has n elements, then it has subsets.

A
2n1
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B
2n
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C
2n1
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D
n
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Solution

The correct option is B 2n

If a set A has one element, say A={a}, then the only subsets of A are {} and {a}. Thus, the set A has 2=21 subsets.
If a set A has two elements, say A={a,b}, then the subsets of A are {}, {a}, {b} and {a,b}. Thus, the set A has 4=22 subsets.
If a set A has three elements, say A={a,b,c}, then the subsets of A are {}, {a}, {b}, {c}, {a,b},{b,c}, {c,a} and {a,b,c}. Thus, the set A has 8=23 subsets.
Similarly, if a set A has n elements, then A will have 2n subsets.


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