# Thread: Members in the Powerset.

1. ## Members in the Powerset.

I have the following 3 sets.

A = {1, 2, 3, 4, 5}, B = {a, b, c, d, e}, C = {red, green, blue}

I want to compute the following $\displaystyle |\wp(A*B*C)|$

So would I first find out how many values are in $\displaystyle A*B*C$

Which I think is $\displaystyle 5*5*3 = 75$

So to compute how many values are in the powerset, would I do $\displaystyle 2^75$? (Should be 2 to the power of 75.)

This gives the result of $\displaystyle 3.77789319 * 10^22$

Am I doing this correct?

2. ## Re: Members in the Powerset.

Originally Posted by richtea9
I have the following 3 sets.
$\displaystyle A = {1, 2, 3, 4, 5}, B = {a, b, c, d, e}, C = {red, green, blue}$
I want to compute the following $\displaystyle |\wp(A*B*C)|$
Your notation is a bit off (i.e. non-standard).
I think that you want $\displaystyle |\mathcal{P}(A\times B\times C)|=2^{|A|\cdot|B|\cdot|C|\cdot}$.

If that is not what you mean, please clear things up.

3. ## Re: Members in the Powerset.

Originally Posted by Plato
Your notation is a bit off (i.e. non-standard).
I think that you want $\displaystyle |\mathcal{P}(A\times B\times C)|=2^{|A|\cdot|B|\cdot|C|\cdot}$.

If that is not what you mean, please clear things up.
Yeah, I want the powerset of the cartesian product of a, b, c (A*B*C).

Are we on the same lines?

4. ## Re: Members in the Powerset.

Originally Posted by richtea9
Yeah, I want the powerset of the cartesian product of a, b, c (A*B*C). Are we on the same lines?
Exactly the same.
So the answer is $\displaystyle 2^{75}$.

5. ## Re: Members in the Powerset.

Originally Posted by Plato
Exactly the same.
So the answer is $\displaystyle 2^{75}$.
Perfect, thought so, thanks for the help.