Respuesta :

That should be 2^n and not just 2n

If we have 4 subsets, then 2^n = 4 leads to n = 2 since 2^2 = 4.

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Here's an example.

A = {p,q}

The four subsets of set A = {p,q} are

  • {p,q} ... any set is a subset of itself
  • {p} .... a set with one element inside it is called a singleton set
  • {q} ... also a singleton set
  • { } ... the empty set, you can use the special symbol [tex]\varnothing[/tex] to denote the empty set

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Here's an example with n = 3 elements. We'll have 2^n = 2^3 = 8 subsets now. Let's say we had B = {r,s,t}

Those 8 subsets of set B are...

  1. {r,s,t}
  2. {r,s}
  3. {r,t}
  4. {s,t}
  5. {r}
  6. {s}
  7. {t}
  8. { } or [tex]\varnothing[/tex]

Note that order does not matter within any given set. Something like {r,s} is the same as {s,r}.

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