# Thread: Number of sets to write

1. ## Number of sets to write

Set A= {a,b,c,d,e}
A U B = {a,b,c,d,e,f,g,h,k,m,n}
Based on this, how many different sets of B can be written ?
I tried 2^6 or 6! But it says answer is 32... why is that ?

2. ## Re: Number of sets to write

Originally Posted by ketanco
I tried 2^6 or 6! But it says answer is 32... why is that ?
2^6 = 64, 6! = 720
Any reason you "tried" these?
Interestingly: 2^5 = 32.

3. ## Re: Number of sets to write

Originally Posted by ketanco
Set A= {a,b,c,d,e}
A U B = {a,b,c,d,e,f,g,h,k,m,n}

Based on this, how many different sets of B can be written ?
I tried 2^6 or 6! But it says answer is 32... why is that ?
Set A doesn't have any of the (last visually listed as above) elements in it, so you're going to have to union {f, g, h, k, m, n}
with every subset of set A down to the empty set to get every different possible set B.

{a,b,c,d,e} U {f, g, h, k, m, n}
.
.
.

{ } U {f, g, h, k, m, n}

There are $\displaystyle \ 2^5 \ = \ 32 \$ of these.