Set theory: find the intersection

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SUMMARY

The discussion revolves around a set theory problem involving a group of 30 people who read books A, B, and C. Specifically, 23 people read book A, 12 read book B, and 23 read book C. Participants expressed confusion regarding the symmetry between books A and C, and the unusual scenario of individuals reading the same book twice. The consensus is that the problem may contain errors, making it difficult to derive accurate intersections between the sets of readers.

PREREQUISITES
  • Understanding of set theory concepts, particularly intersections
  • Familiarity with Venn diagrams for visualizing relationships between sets
  • Basic knowledge of problem-solving strategies in combinatorics
  • Ability to interpret and analyze mathematical word problems
NEXT STEPS
  • Study set theory intersections and their applications in problem-solving
  • Learn how to construct and interpret Venn diagrams for three sets
  • Explore combinatorial counting techniques to handle overlapping sets
  • Review common pitfalls in word problems involving multiple conditions
USEFUL FOR

Students studying mathematics, particularly those focusing on set theory and combinatorics, as well as educators seeking to clarify complex problem-solving techniques.

Matt_92
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Homework Statement



In a group of 30 people each person twice read a book from books A, B, C. 23 people read book A, 12 read book B and 23 read book C.

(a) How many people read books A and B?
(b) How many people read books A and C?
(c) How many people read books B and C?

Homework Equations





The Attempt at a Solution



I'm not sure how to start. Any hints will be very much appreciated.
Thank you
 
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There seem to be errors with this problem. For example, the problem is symmetric in A and C, so parts (a) and (c) are really the same question. And usually people don't read the same book twice but that seems to happen here. I would ignore this problem for being unclear or having errors.

Also, in the current form it looks prohibitively difficult to solve, suggesting that there is a mistake.
 
Matt_92 said:

Homework Statement



In a group of 30 people each person twice read a book from books A, B, C. 23 people read book A, 12 read book B and 23 read book C.

(a) How many people read books A and B?
(b) How many people read books A and C?
(c) How many people read books B and C?

Homework Equations





The Attempt at a Solution



I'm not sure how to start. Any hints will be very much appreciated.
Thank you

Welcome to the PF

Please check your PMs -- you *must* show some effort toward solving the problem before we can offer tutorial help
 

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