Question 11.Taking a(x), b(x) and c(x) to denote thestatements "x E A”, “x € B" and "x E C" respectively, write each of thefollowing as a proposition in predicate logic, then prove the proposition isvalid.(a) AUB=AU (B - A)(b) (AUB) ≤ C = (A ≤C) ^ (B ≤ C)

Given: A∪B=A∪B-A A∪B⊆C≡A⊆C∧B⊆C ax, bx, and cx denotes x∈A, x∈B, and x∈C respectively. To do:…

Answered: Question 11. Taking a (x), b(x) and…

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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Question 11. Taking a (x), b(x) and c(x) to denote the statements "x E A", "x E B" and "x E C" respectively, write each of the following as a proposition in predicate logic, then prove the proposition is valid. (a) AUB=AU (B − A) (b) (AUB) ≤ C = (A ≤ C) A (B≤ C)