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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}
A ∩ B ∩ C = {} ?

  Submitted by DJ    
Rating: 4.3636 (11 votes)
Solution: (Hide)

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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: Is this right ?Penny2004-02-10 16:47:23
Some Thoughtsre(5): Solution FINAL WORD revisitedAdy TZIDON2004-02-10 16:38:55
re(5): Solution FINAL WORD(by CharlieCharlie2004-02-10 15:58:42
re(4): Solution FINAL WORD(by CharlieCharlie2004-02-10 15:53:24
re(4): Solution FINAL WORDBrian Smith2004-02-10 15:13:44
re(3): Solution FINAL WORD(by CharlieAdy TZIDON2004-02-10 14:50:41
re(2): Solution FINAL WORDCharlie2004-02-10 13:30:02
re(2): Solution - not yet?Charlie2004-02-10 13:24:41
QuestionIs this right ?Penny2004-02-10 13:02:43
Some Thoughtsre: Solution FINAL WORDAdy TZIDON2004-02-10 13:01:06
re(3): Game, set and match !!!!SilverKnight2004-02-10 12:14:34
re(2): Game, set and match !!!!Penny2004-02-10 12:08:54
re: Game, set and match !!!!SilverKnight2004-02-10 11:39:29
Game, set and match !!!!Penny2004-02-10 11:31:50
re: Solution - not yet?SilverKnight2004-02-10 11:26:26
re(3): solutionSilverKnight2004-02-10 11:13:33
re(4): my solutionAdy TZIDON2004-02-10 11:12:54
re: Solution - I'll drink to thatAdy TZIDON2004-02-10 11:10:41
re(3): my solutionCharlie2004-02-10 11:07:22
re(2): solutionCharlie2004-02-10 11:00:46
re(2): solutionAdy TZIDON2004-02-10 11:00:42
re(2): my solutionAdy TZIDON2004-02-10 10:58:51
SolutionBrian Smith2004-02-10 10:58:38
re: solutionSilverKnight2004-02-10 10:56:23
Some Thoughtsre: solutionAdy TZIDON2004-02-10 10:55:19
re: solutionPenny2004-02-10 10:52:13
re: my solutionCharlie2004-02-10 10:52:08
Hints/TipsPenny u r overlooking something again :-(Ady TZIDON2004-02-10 10:47:56
SolutionsolutionCharlie2004-02-10 10:45:08
Solutionmy solutionAdy TZIDON2004-02-10 10:33:08
SolutionSolution, unless I am overlooking something again :-(Penny2004-02-10 10:20:37
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