Math Questions on Sets?

Question

1) List all the non-empty proper subsets of the set W= {a, {a,b}, Θ}

2) If U= {1,2,3,...20} and A= {2,4,6,...20} find n(A')

3) The number of proper subsets of H is 524,287. What is the n(H)?

I am still not sure what the answer to question number 1 is. Everyone is giving me different answers.

2) N(A') = 10

3) I figured this question out. Everyone else said it was impossible. Anyway the solution is:

524287 + 1 = 524288
2^x = 524288
x = 19
therefore, n(H) = 19

Now can someone help me with question number 1 please ... I need all the subsets listed and I am not sure whether or not to include theta because it says "non-empty proper subsets".

Answer 1

#1

There are 8 subsets here: your set has six things in it, and there are 2^3 subsets.

{ }
{a}
{ {a,b} }
{θ}
{ a , {a,b} }
{ a , Θ }
{ Θ , {a,b} }
{ a , {a,b} , Θ }

We exclude the empty set and W itself. That's 8-2=6.

#2

Here, you don't want to find A'. Just use this:

n(A) + n(A') = n(U)

You already have A and U, and there are 10 and 20 in each. So:

n(A') = n(U) - n(A) = 20 - 10 = 10.

#3

The number of proper subsets of H is:

2 ^ (n(H)) - 1

From that, we have:

n(H) = log2(524288) = 19

That's a logarithm base 2.

Answer 2

1) Your responders failed to understand that {theta} is a legitimate set. Since W is a set with three elements, there are 2^3 = 8 subsets, counting phi (the empty set) and the whole set, so we should expect to find 6 subsets : {a}, {{a,b}}, {theta}, {a,{a,b}}, {a,theta}, {{a,b},theta}.

2) A' meaning the complement of A? Then A' = {1,3,...,19}and you have enough fingers to count the size of A'.

3) Whoa! The numer of all subsets of a set with n elements is 2^n, and usually the null set and the entire set are considered improper. So you want us to believe there is a set with 524,287 + 2 = 524,289 being a power of 2???

Answer 3

1. Disregard theta since it is empty. Therefore, {a}, {(a,b}} and {a, {a,b}} are the proper subsets of W.

2. n(A')= n{1,3,5,...,19}=10.

3. Impossible to tell.

Answer 4

1) {a}, { {a,b} },
I have omitted the null set because it is the subset of every set by default.
2)n(A)={1,3,5,7,9,11,13,15,17,19}

Answer 5

i'd relly wanna help you but i don't understand the simbols. and i'm not a native nglish speaker. :((