Let A = {7m +1 : m € Z} and B = {14n – 6 : n € Z} be subsets of a universal set U. Justify why A ¢ B by providing a counterexample with a brief explanation. For part b., no justification is needed. i. List 2 different elements of the set ANB (one in each box): and

Let A = {7m +1 : m € Z} and B = {14n – 6 : n € Z} be subsets of a universal set U. Justify why A ¢ B by providing a counterexample with a brief explanation. For part b., no justification is needed. i. List 2 different elements of the set ANB (one in each box): 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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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Q4. Let A = {7m +1: m € Z} and B = {14n – 6 : n e Z} be subsets of a universal set U.
a. Justify why A ¢ B by providing a counterexample with a brief explanation.
b. For part b., no justification is needed.
i. List 2 different elements of the set ANB (one in each box):|
and
ii. List 2 different elements of the set A×B (one in each box):
and
c. Prove that BC A using a rigorous proof.

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