MHB Sets: A,B,C - Intersection & Difference

AI Thread Summary
The discussion confirms that for three sets A, B, and C, the expression A(B\C) equals (AB)\C and also equals B(A\C). This equality is derived from the definition of set difference. All three expressions ultimately represent the intersection of sets A and B with the complement of set C, denoted as A∩B∩C̅. The participants agree on the correctness of these set operations. Understanding these relationships is essential for working with set theory effectively.
Fermat1
Messages
180
Reaction score
0
Am I right in thinking that if we have 3 sets A,B,C, then with A intersect B represented as AB, we have:

A(B\C)=(AB)\C=B(A\C)?
 
Mathematics news on Phys.org
Yes. This follows from the definition of set minus.
 
All three sets equal $A\cap B\cap\bar{C}$ where $\bar{C}$ is the complement of $C$.
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

MHB Parallelogram ABCD: Finding AC from PB & PD
Replies
1
Views
1K
B Strange quadratic manipulation
Replies
6
Views
2K
MHB Find maximum area of a triangle
Replies
1
Views
1K
B How to draw a plane intersecting a cylinder at a "compound angle"
Replies
8
Views
3K
I The number of intersection graphs of ##n## convex sets in the plane
Replies
2
Views
1K
MHB Λ and μ are scalars, find the value of λ and the value of μ
Replies
4
Views
2K
I Eccentric anomaly of ellipse-circle intersections
Replies
4
Views
2K
MHB Geom Ch: Prove $AB=x^3$ Given $\triangle ABC$ & $\triangle AEF$
Replies
1
Views
1K
MHB Difference of angles in a triangle
Replies
4
Views
2K
MHB Positive Integers: Evaluate $a+b+c$
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top