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

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SUMMARY

The discussion centers on proving the mathematical statement (A=B ∪ C and B ∩ C=Ø) => (A\B=C). Participants emphasize the importance of understanding that this is a proposition rather than an equation. A Venn diagram is suggested as a visual aid to clarify the relationships between the sets involved. The conversation highlights the need for formal proof techniques in set theory.

PREREQUISITES
  • Understanding of set theory concepts, including unions and intersections.
  • Familiarity with Venn diagrams for visual representation of set relationships.
  • Knowledge of formal proof techniques in mathematics.
  • Basic terminology in mathematical logic, including propositions and implications.
NEXT STEPS
  • Study formal proof techniques in set theory.
  • Learn how to construct and interpret Venn diagrams for complex set relationships.
  • Explore the implications of set operations in mathematical logic.
  • Review definitions and examples of mathematical propositions and theorems.
USEFUL FOR

Mathematics students, educators, and anyone interested in formal proofs and set theory concepts will benefit from this discussion.

Violet1
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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
.
 
:(
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?
 

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