Determine the number of subsets of a set with 7 elements.

Question

This would be 128, I believe. Is this correct?

Answer 1

Yes, I believe it is. For each subset it can either contain or not contain an element. For each element, there are $2$ possibilities. Multiplying these together we get $2^7$ or $128$ subsets.

Answer 2

For generalisation the total number of subsets of a set containing n elements is 2 to the power n. And you are surely right.

Answer 3

Each subset can be represented by a function f from the set itself, call it $X $, into a $2$ element set ( say $\{0,1\} $), with $f(x)=1$ if $x\in X $ is in the subset and $f (x)=0 $ if not. Thus we have the function space, $Y^X $, of functions from $X $ to $Y $, known as the power set when $Y $ is a two element set. Its order is of course $2^7$, or $2^{|X|}$ in general. ..

Answer 4

You can probably count how many subsets are in a set with one "object", or at least, that's what I call it. There is only one subset in the set. When there are two objects, you get 3 subsets. When there are 3 objects, you get 7 subsets. When there are 4 objects, if you want to count it, it has 15 subsets. Basically, at this point, we can conclude a statement: "For every amount $n$ in a set, there will be $2^n-1$ subsets as a result. You can count for yourself if you don't believe it, but I don't recommend it!