Question

List the number of proper subsets of the set { 3,4,6,8}

Answer 1

choices are
15
16
17
none of the above

Answer 2

Let's ignore the word proper for a moment.
Do you remember how to count the number of `subsets` of a set? :)
It has something to do with powers of 2.

Answer 3

I remember sort of

Answer 4

16?

Answer 5

So let's first figure out the number of `subsets` of our set.
We'll go on to `proper subsets` after that.

2 raised to the power of the `cardinality of the set` gives us the number of subsets of the set.

Cardinality is just the `number of elements` in the set.
We have 4 elements.
So 2^4 = 16.

Good.

But that's `subsets`,
now for the restriction of `proper subsets`.

Answer 6

The subset { 3, 4, 6, 8 } is NOT a proper subset.
But every other subset is.

Answer 7

The subset that is equal to itself, can't be proper.

Answer 8

Okay

Answer 9

So we need to subtract 1 from our total,
simple as that! :)

Answer 10

Thanks(:

Answer 11

np