please send handwritten solution for Q 3 Problem 1: Prove A = {m € Z : m mod 6 = 2} is a proper subset of B = {n EZ:n is even}.Problem 2: Shade a Venn diagram to represent the sets A, B, and C, such that:(i) C – (AªN B)(ii) ANB = Ø and AnC= CProblem 3: Use the set identities/laws to show (A – Bº) U (ACU B)° = A.Problem 4: Recall that the power set P(A) is the set of all subsets of A. Prove that if A C BnC and B C C,then P(A) U P(B) C P(C).

Answered: Image /qna-images/answer/bcab3050-99e6-48b8-996f-87bb8627e2b7.jpg

Answered: Problem 3: Use the set identities/laws…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 10AEXP

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Problem 3: Use the set identities/laws to show (A- Bº)U (A° U B)e = A.