How many subsets does a set A={a,b,c,d} have
Answers
Step-by-step explanation:
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.
Answer:
A set having n members has 2n subsets. This number includes the empty set and the given set.
The set A has 4 members, so it has
2⁴=16 subsets.
They are:
∅={ }, {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}, {a, b, c, d}.
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