Solving Sets: (A intersects B) - C

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Homework Help Overview

The problem involves set operations, specifically the expression (A intersects B) - C, with the sets defined as A= {1,4,7,10}, B= {1,2,3,4,5}, and C= {2,4,6,8}. The original poster seeks clarification on the correct application of set difference after determining the intersection of sets A and B.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply the order of operations to find the intersection of sets A and B, leading to the result {1, 4}. They then express uncertainty about the subsequent operation of subtracting set C. Other participants question the understanding of set difference and encourage applying the definition to the specific sets involved.

Discussion Status

The discussion is ongoing, with participants providing guidance on the definition of set difference and prompting the original poster to reconsider their interpretation of the elements involved. There is an acknowledgment of a misunderstanding regarding which elements belong to set C.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the amount of direct assistance provided. The original poster's confusion highlights the importance of correctly applying definitions in set theory.

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Homework Statement


Here is the problem that I want to make sure I have an understanding of:

(A intersects B) - C

Given the following sets: A= {1,4,7,10} B= {1,2,3,4,5} C= {2,4,6,8}

Order of operations tells me to do what's in parentheses first. A intersecting B which gives me {1, 4}

Now minus C is where I'm a little fuzzy - I think the final answer is {4} because I took out the number that wasn't in set C - being 1.

Am I on the right track?
 
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What is the definition of X\Y or X-Y in your notes?
 
The difference X - Y consists of all elements in X that are not in Y
 
So apply the definition to the sets.
 
Right - so the answer is 4
 
?
YOU just said "The difference X - Y consists of all elements in X that are not in Y" (added emphasis). So (A intersect B)- C consists of all elements of (A intersect B) that are not in C. And C= {2, 4, 6, 8}.
Which of 1 and 4 is not in C?
 
Okay - I had it backwards - 1 is not in C
 

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