1. ## Power Set question.

Hello all =)

i am strugling (?) here with some old homework...

lets see...

A=P({a,c,d,e,g}) , B=P({c,d,e,f,g}) . ( P(X) is the power set of X) .

Calculate |A U B| .

My thoughts are:

A= 2^5= 32
B= 2^5= 32

|A U B| i believe that, it should be for example a new set that contains {a,c,d,e,f,g}
so thats 2^6=64

Right?

If its right, is this a good way to type as an answer?

Thanks for your time, and assistance =)

2. Originally Posted by primeimplicant
Hello all =)

i am strugling (?) here with some old homework...

lets see...

A=P({a,c,d,e,g}) , B=P({c,d,e,f,g}) . ( P(X) is the power set of X) .

Calculate |A U B| .

My thoughts are:

A= 2^5= 32
B= 2^5= 32

|A U B| i believe that, it should be for example a new set that contains {a,c,d,e,f,g}
so thats 2^6=64

Right?

If its right, is this a good way to type as an answer?

Thanks for your time, and assistance =)
You will need to rethink your answer because A U B does not contain {a,c,d,e,f,g}.

I recommend considering P({a,c,d,e,f,g}) and removing those sets that are supersets of {a,f}.

3. $\displaystyle \left| {A \cup B} \right| = \left| A \right| + \left| B \right| - \left| {A \cap B} \right|$.

But is that $\displaystyle 2^5+2^5-2^4?$

4. Originally Posted by Plato
$\displaystyle \left| {A \cup B} \right| = \left| A \right| + \left| B \right| - \left| {A \cap B} \right|$.

But is that $\displaystyle 2^5+2^5-2^4?$
I'm not sure if your question was directed at me but both our methods yield the same answer.

$\displaystyle 2^5+2^5-2^4 = 2^6 - 2^4$

Edit: I misread something so the wording of this post came out kind of funny, carry on..

5. Originally Posted by undefined
I'm not sure if your question was directed at me but both our methods yield the same answer.
Actually no, was just commenting on the usual formula.

$\displaystyle \displaystyle |P(J)\cup P(K)|=2^{|J|}+2^{|K|}-2^{|J\cap K|}}.$

6. hah,

thanks a lot , now it makes sense !

thanks again.

7. Originally Posted by primeimplicant
hah,

thanks a lot , now it makes sense !

thanks again.
Well in case you didn't understand my first post and would like to: A U B contains precisely those elements of P({a,c,d,e,f,g}) that do not contain {a,f}, since no element of A contains {a,f} and no element of B contains {a,f}. (The first "contains" means set membership and the other "contain(s)" mean subset.)