number of subsets, proper subsets, of 9-element set

A set contains 9 elements.

a) How many subsets does it have?
b) How many proper subsets does it have?

a) What's the formula they gave you for the number of subsets, proper or otherwise, of an n-element set?

b) What is the definition of a "proper" subset? How many of the subsets counted in (a) will not be "proper"? So how many will be?

Thank you!

Eliz.

a) The non-negative integers smaller than 9, wouldn't it be?

patti72458 said:

A set contains 9 elements.

a) How many subsets does it have?
b) How many proper subsets does it have?

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You might want to start by using some simpler sets to see if you can find a pattern.

If A = { } (or, A is the empty set) how many subsets does it have? Just 1....the empty set

If A = { 1 },how many subsets does it have? Well, there is one subset with NO elements (the empty set), and 1 subset with just one element. So, if the original set has one element, there are TWO subsets.

Ok...now continue this investigation. See if you can find a pattern relating the number of elements in the original set, and the number of subsets of that set.

If you are still having trouble with this problem, please repost, showing us what you've tried. If we can see what you're thinking, we can better be able to help you.

morson said:

a) The non-negative integers smaller than 9, wouldn't it be?

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There is nothing saying that the elements are whole numbers. One could equate the elements to these, if desired, of course, but this isn't necessary.

And the exercise doesn't ask for a listing of the elements in the various subsets, only for the number of such subsets. Using the formulas the poster was given in class should do the trick!

Eliz.