MHB Sets: A,B,C - Intersection & Difference

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The discussion confirms that for three sets A, B, and C, the expression A(B\C) equals (AB)\C and also equals B(A\C). This equality is derived from the definition of set difference. All three expressions ultimately represent the intersection of sets A and B with the complement of set C, denoted as A∩B∩C̅. The participants agree on the correctness of these set operations. Understanding these relationships is essential for working with set theory effectively.
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Am I right in thinking that if we have 3 sets A,B,C, then with A intersect B represented as AB, we have:

A(B\C)=(AB)\C=B(A\C)?
 
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Yes. This follows from the definition of set minus.
 
All three sets equal $A\cap B\cap\bar{C}$ where $\bar{C}$ is the complement of $C$.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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