MHB Drawing the Venn Diagram for A ∩ Bc

AI Thread Summary
The discussion focuses on drawing the Venn diagram for the intersection of set A and the complement of set B (A ∩ Bc). Participants confirm that the solution presented is correct, emphasizing that A ∩ Bc can be expressed as A - B. There is clarification that nothing outside of sets A and B should be shaded in the diagram. The conversation highlights the importance of understanding the regions defined by both A and B's complement. Overall, the participants agree on the correct interpretation and representation of the sets involved.
WannaBe
Messages
11
Reaction score
0
Draw the venn diagram for A∩Bc

(A Intersection B Completement)

Is my solution correct?

View attachment 1524
 

Attachments

  • A-B.png
    A-B.png
    2.2 KB · Views: 114
Physics news on Phys.org
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.
 

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
View full post »

Similar threads

B Do any 3D Venn diagrams exist that have no 2D analogues?
Replies
3
Views
1K
I Implication, Boolean Expression and Venn Diagrams
Replies
12
Views
7K
MHB Venn diagram and table word problem Help
Replies
1
Views
2K
MHB Venn Diagram: p v (q ^ r) = (p v q) ^ (p v r)
Replies
1
Views
3K
I This would be a false statement, correct?
Replies
6
Views
2K
B Cant get Venn diagram to agree with Demorgan's Law
Replies
10
Views
2K
MHB How Do Truth Tables and Venn Diagrams Verify Logical Equivalence?
Replies
1
Views
3K
MHB Venn Diagram II: Check Answers & Understand Relationships
Replies
11
Views
3K
MHB Operations on Sets: Proving A⊆B⊆C & A∪B=B∩C
Replies
2
Views
2K
I Venn diagram for the reals and transfinite numbers as sets
Replies
10
Views
3K

Hot Threads

Recent Insights

Back
Top