# Finding specific sets

I'm trying to calculate these particular sets given that:

$$A=\{a,c,e,h,k\}$$ $$B=\{a,b,d,e,h,i,k,l\}$$ $$C=\{a,c,e,i,m\}$$

$$A \cap B$$

$$A\cap B \cap C$$

$$A \cup B \cup C$$

$$A-B$$

$$A-(B-C)$$

Thanks!

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The set $A^{B^C}$ has $5^{32768}$ elements; this is a number with 22,903 digits. So it is impossible to list the elements of that set explicitly. Even $A^B$, with only $5^8 = 390,625$ elements, is too big to conveniently list. What do you mean when you say you want to "calculate the set"? – MJD Feb 11 '13 at 20:10

$A \cap B = \{a,e,h,k\}$

$A \cap B \cap C = \{a,e\}$

$A \cup B \cup B = \{a,b,c,d,e,h,i,k,l,m\}$

$A \setminus B = \{c\}$

$A \setminus \{B\setminus C\} = A\setminus \{b,d,h,k,l\} = \{a,c,e\}$

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You sure on those last two? – user61867 Feb 11 '13 at 19:57
Yes, I am. What's the problem? – azimut Feb 11 '13 at 20:02
Misread it. Got something different. All good now. Thanks! – user61867 Feb 11 '13 at 20:04
Please accept this as the correct answer to give me some reputation points. – azimut Feb 11 '13 at 20:04