Verifying Identity: Easier Way to Solve?

  • Thread starter autre
  • Start date
  • Tags
    Identity
In summary, the conversation discusses verifying the identity (A\B)\DeltaC = (A\DeltaC)\Delta(A\bigcapB) and the use of Venn diagrams to solve it. The speaker has tried a brute force method and found it cumbersome, but has now found success using Venn diagrams.
  • #1
autre
117
0
I need to verify this identity:

(A\B)[itex]\Delta[/itex]C = (A[itex]\Delta[/itex]C)[itex]\Delta[/itex](A[itex]\bigcap[/itex]B)

(with delta standing for the symmetric difference, I don't know the proper latex code) I've tried it "brute force" several times, working out each side and simplifying it until the sides are equal (it's likely that I'm messing up a negation somewhere) and I've found this method rather cumbersome. Is there any simpler way to solve this?
 
Physics news on Phys.org
  • #2
Hi autre! :smile:

Have you tried drawing a so called Venn diagram?
 
  • #3
I used Venn diagrams and got the result you are looking for. There are 7 disjoint sets involved. Is that the brute force you tried?
 
  • #4
That's it, mathman. Thanks guys.
 
  • #5


I understand your frustration with the cumbersome process of verifying this identity. However, it is important to note that some mathematical concepts may require a more detailed and meticulous approach in order to ensure accuracy and rigor.

In this case, the use of brute force may not be the most efficient method to verify this identity. Instead, I would recommend breaking down the problem into smaller components and using established mathematical principles and properties to solve it.

First, we can rewrite the left side of the identity as (A∩B')∪(B∩A')∪(C∩A∩B'), where ' indicates complement. Similarly, the right side can be rewritten as (A∩B')∪(B∩A')∪(A∩B∩C').

Next, we can use the distributive property of set operations to rearrange the terms on both sides. This will give us (A∩B')∪(B∩A')∪(A∩B∩C') = (A∩B')∪(A∩B∩C')∪(B∩A').

Now, we can use the commutative and associative properties to rearrange the terms further and see that both sides are equal to A∩(B'∪C')∪(B∩A').

Finally, we can use the definition of the symmetric difference (A△B = (A∪B)∩(A∩B)') to rewrite the terms in terms of the symmetric difference. This will give us A∩(B'∪C')∪(B∩A') = (A△B')∪(B△A')∪(A∩B∩C') = (A△B')∪(A△B∩C') = (A△B')∪(A△C∪B) = (A△B')∪(A△C)∪(B△A) = (A△B)△(A∩C) = (A△C)△(A∩B) = (A△C)∩(A∩B)' = (A△C)∩(B'∪A') =
 

1. What is identity verification?

Identity verification is the process of confirming that an individual is who they claim to be. This can involve verifying personal information, such as name, date of birth, and address, through various methods such as documents, biometrics, or behavioral data.

2. Why is identity verification important?

Identity verification is important for security and fraud prevention purposes. By verifying a person's identity, organizations can ensure that the person they are interacting with is who they claim to be, reducing the risk of identity theft and fraudulent activities.

3. What is an easier way to verify identity?

An easier way to verify identity is through the use of digital identity verification methods. This involves using technology, such as biometric scanning or document verification software, to quickly and accurately verify a person's identity without the need for manual processes.

4. What are the benefits of using digital identity verification?

Digital identity verification offers several benefits, including increased efficiency, improved accuracy, and enhanced security. It can also help reduce the costs and time associated with traditional identity verification methods.

5. How can identity verification be used in different industries?

Identity verification can be used in various industries, including finance, healthcare, government, and e-commerce. In finance, it can help prevent fraud and comply with regulations. In healthcare, it can ensure patient data is secure. In government, it can help with citizen identification and access to services. In e-commerce, it can help prevent identity theft and ensure secure transactions.

Similar threads

A Solving the Radial Equation for the Dirac Hydrogen Atom Solution
    • Quantum Physics
Replies
10
Views
2K
Correct numerical modeling of the 3D Dirac Delta function
    • Programming and Computer Science
Replies
13
Views
3K
Having trouble verifying a trig identity.
    • Precalculus Mathematics Homework Help
Replies
4
Views
2K
Is there an easier way to solve rational equations?
    • General Math
Replies
5
Views
2K
Powers with fractional exponents that have an even denominator
    • Precalculus Mathematics Homework Help
Replies
13
Views
2K
I Toppling a Hemisphere: Solving for Kinetic Energy in a Delicate Collision
    • Classical Physics
Replies
2
Views
1K
Is this algorithm stable? (time dependent diffusion equation)
    • Programming and Computer Science
Replies
2
Views
2K
I Solving the Basel problem using Gauss's law
    • General Math
Replies
4
Views
2K
The Philosophy of Proving Trig Identities
    • General Math
Replies
4
Views
8K
I Attempting to find an intuitive proof of the substitution formula
    • Calculus
Replies
7
Views
1K

Hot Threads

Recent Insights

Back
Top