To demonstrate set union and intersection to her class, Mrs. Putnam asked for three students to each write down a set of numbers.
After they had done so, she looked at their sets and told the class, "the union of these three sets is the first ten counting numbers, but their intersection is empty!"
How many triples (A, B, C) of sets are there such that
A U B U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
and
A ∩ B ∩ C = {} ?
(In reply to
re: Game, set and match !!!! by SilverKnight)
Maybe I should just ride into the subset.....
(A int B) int C = {}
If C has just 1 number (there are 10 such sets), then any two sets A and B, where A is any subset of the remaining 9 numbers, and B is any subset of all 10 numbers, should do the trick. A set of 9 elements has 2^9 subsets. A set of 10 elements has 2^10 subsets.
(10)*(2^9)*(2^10)=5242880
If C has just 2 numbers (there are 10*9 such sets), then any two sets A and B, where A is any subset of the remaining 8 numbers, and B is any subset of all 10 numbers, will work. A set of 8 elements has 2^8 subsets.
(10*9)*(2^8)*(2^10)=23592960
If C has just 3 numbers (there are 10*9*8 such sets), then any two sets A and B, where A is any subset of the remaining 7 numbers, and B is any subset of all 10 numbers, will work.
(10*9*8)*(2^7)*(2^10)=94371840
But the numbers begin to overwhelm my primitive calculator.........
Edited on February 10, 2004, 12:10 pm

Posted by Penny
on 20040210 12:08:54 