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Set Me Up (Posted on 2004-02-10) Difficulty: 3 of 5
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 = {} ?

See The Solution Submitted by DJ    
Rating: 4.3636 (11 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution - not yet? | Comment 17 of 31 |
(In reply to Solution by Brian Smith)

Brian,

I don't understand the second half of your 'solution'.
You wrote:
"There are 3^10 triplets with A empty, likewise for B and C. The set with A, B empty was counted twice, likewise with A, C and B, C.

The total number of triplets with empty sets is 3*3^10-3 = 177144
"

I don't believe you properly accounted for the requirement that the intersection of all three MUST be the null set.

- SK
  Posted by SilverKnight on 2004-02-10 11:26:26

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