Question

A set of n elements has 2n subsets. Our set has 4 subsets. Thus, we have the equation
2n =

Answer 1

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
  `\varnothing` 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
   `\varnothing`

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