MHB Proofing the Equation: (A=B Union C & B ∩ C=Ø) => (A\B=C)

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The discussion revolves around proving the mathematical statement (A=B union C and B intersect C=Ø) implies (A\B=C). Participants emphasize the importance of understanding the concepts involved, suggesting the use of Venn diagrams to visualize the relationships between sets. One user points out that the original request mislabels the statement as an equation rather than a theorem. The conversation encourages a deeper exploration of formal proof techniques, with a focus on clarity and logical reasoning. Overall, the thread highlights the value of visual aids and precise language in mathematical discussions.
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Hi! I need help for this:
Proof equation: (A=B union C and B intersect C=empty set)=>(A\B=C)!

Tnx! :o
 
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Hi and welcome to the forum.

What kind of help do you need? Surely you understand that if you take all women from a group of adults, you'll get all men and only men.

Please take some time to read the http://mathhelpboards.com/rules/, especially rule #11. Also, what you are proving is not an equation; it's a statement (claim, proposition, theorem) in the form of an implication. Finally, "proof" is a noun, and the corresponding verb is "prove".
 
Heh :D Perhaps Evengy overdid it a bit.

Okay, try drawing the Venn diagram. What do you observe? Do you see how obvious it is? Can you now sketch out a formal proof?

Balarka
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:(
mathbalarka said:
Heh :D Perhaps Evengy overdid it a bit.

Okay, try drawing the Venn diagram. What do you observe? Do you see how obvious it is? Can you now sketch out a formal proof?

Balarka
.

Thanks Balarka! When I draw Venn diagram, everything is clear! But I can't sketch out a formal proof! :(
 
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Perhaps you could at least show us what approach you took?
 

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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