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Prove the following equality is true. VA, B,C EU, (BCC A) → (C − A) n (B − A) = Ø

Prove the following equality is true. VA, B,C EU, (BCC A) → (C − A) n (B − A) = Ø

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Proof must follow the form of the proof method "set element method for proving a set equals the empty set"

The method requires the instantiation of an element in a set that is claimed to be empty and a proof by contradiction that the set is empty.

Please give the proof line by line, with each line being a statement and a justification.

Please give the proof in English, not just math symbols, so I can use the proof for study. 

Formally start and end the proof. 

Thank you!

Prove the following equality is true. VA, B, C = U, (BNC ≤ A) → (C − A) ^ (B − A) = Ø
Transcribed Image Text:Prove the following equality is true. VA, B, C = U, (BNC ≤ A) → (C − A) ^ (B − A) = Ø
Expert Solution
Step 1

Let, A, B, C be three sets such that

        B ∩ C ⊆ A

Now, if possible, let, 

      x ∈ (C – A) ∩ (B – A) 

       => x ∈ (C – A)    and     x ∈ (B – A) 

       => (x ∈ C but x ∉ A)  and   (x ∈ B but x ∉ A) 

   

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