Drawing the Venn Diagram for A ∩ Bc

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SUMMARY

The discussion focuses on the Venn diagram representation of the intersection of set A and the complement of set B, denoted as A ∩ Bc. Participants confirm that the solution A ∩ Bc = A - B is correct, indicating that no shading occurs outside the sets A and B within the universal rectangle. The conversation emphasizes the importance of understanding the relationship between sets and their complements in set theory.

PREREQUISITES
  • Understanding of set theory concepts, specifically intersections and complements.
  • Familiarity with Venn diagrams for visual representation of sets.
  • Basic knowledge of mathematical notation related to sets.
  • Ability to interpret graphical representations of mathematical concepts.
NEXT STEPS
  • Study the properties of set complements in detail.
  • Learn how to construct Venn diagrams for multiple sets.
  • Explore advanced topics in set theory, such as De Morgan's laws.
  • Practice problems involving set operations and their visual representations.
USEFUL FOR

Students, educators, and anyone interested in mathematics, particularly those studying set theory and its applications in logic and probability.

WannaBe
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Draw the venn diagram for A∩Bc

(A Intersection B Completement)

Is my solution correct?

View attachment 1524
 

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Yep, looks good. (Yes)
 
Jameson said:
Yep, looks good. (Yes)
Thank You.

A∩Bc = A-B

So, we don't shade anything in the Universe (rectangle) right? (i.e. outside of A and B)
 
WannaBe said:
Thank You.

A∩Bc = A-B

So, we don't shade anything in the Universe (rectangle) right? (i.e. outside of A and B)

Correct. You're thinking in the right way considering events outside of $A$ and $B$ though. For example, $B^c$ is part of $A$ and everything outside the two circles. However, when we see what is both in $A$ and this region, $B^c$, it is in fact the region you have highlighted in red.
 

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