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 $C$.
 

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