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 Set Me Up (Posted on 2004-02-10)
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 = {} ?

 Submitted by DJ Rating: 4.3636 (11 votes) Solution: (Hide) 610 There are six possibilities for which set(s) each element (1-10): just A, just B, just C, not A (meaning B and C, but not A), not B, or not C. The first answer many people arrive at is 310, thinking that each number can belong to just one of the students, but each could also end up in two of the sets (as long as it's not in all three, it won't be in the intersection). While one (or two) of the students would probably not be expected to have specified the null set, nothing in the problem precludes that possibility.

 Subject Author Date re: Is this right ? Penny 2004-02-10 16:47:23 re(5): Solution FINAL WORD revisited Ady TZIDON 2004-02-10 16:38:55 re(5): Solution FINAL WORD(by Charlie Charlie 2004-02-10 15:58:42 re(4): Solution FINAL WORD(by Charlie Charlie 2004-02-10 15:53:24 re(4): Solution FINAL WORD Brian Smith 2004-02-10 15:13:44 re(3): Solution FINAL WORD(by Charlie Ady TZIDON 2004-02-10 14:50:41 re(2): Solution FINAL WORD Charlie 2004-02-10 13:30:02 re(2): Solution - not yet? Charlie 2004-02-10 13:24:41 Is this right ? Penny 2004-02-10 13:02:43 re: Solution FINAL WORD Ady TZIDON 2004-02-10 13:01:06 re(3): Game, set and match !!!! SilverKnight 2004-02-10 12:14:34 re(2): Game, set and match !!!! Penny 2004-02-10 12:08:54 re: Game, set and match !!!! SilverKnight 2004-02-10 11:39:29 Game, set and match !!!! Penny 2004-02-10 11:31:50 re: Solution - not yet? SilverKnight 2004-02-10 11:26:26 re(3): solution SilverKnight 2004-02-10 11:13:33 re(4): my solution Ady TZIDON 2004-02-10 11:12:54 re: Solution - I'll drink to that Ady TZIDON 2004-02-10 11:10:41 re(3): my solution Charlie 2004-02-10 11:07:22 re(2): solution Charlie 2004-02-10 11:00:46 re(2): solution Ady TZIDON 2004-02-10 11:00:42 re(2): my solution Ady TZIDON 2004-02-10 10:58:51 Solution Brian Smith 2004-02-10 10:58:38 re: solution SilverKnight 2004-02-10 10:56:23 re: solution Ady TZIDON 2004-02-10 10:55:19 re: solution Penny 2004-02-10 10:52:13 re: my solution Charlie 2004-02-10 10:52:08 Penny u r overlooking something again :-( Ady TZIDON 2004-02-10 10:47:56 solution Charlie 2004-02-10 10:45:08 my solution Ady TZIDON 2004-02-10 10:33:08 Solution, unless I am overlooking something again :-( Penny 2004-02-10 10:20:37

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