76 CHAPTER 2 Sets and Whole Numbers 11. Let G n n divides 90) and D listed form, G = (1,2,3,5,6. 9, 10, 15, 18, 30, 45,90) (nn divides 144). In (a) Find the listed form of the set D. (b) Find G n D (c) Which element of G nD is largest? 12. Draw and shade Venn diagrams that correspond to the following sets: (b) AU (BnC (d) AU (BnC) (f) An BnC (а) А ОВГС (c) (An B) UC (e) AUBUC 13. For each part, draw a Venn diagram whose loops for sets A, B. and C show that the conditions listed must hold. (a) AC C, B C C,AnB= (b) СС (АПВ) (c) (An B) CC 14. If A U B = AUC, is it necessarily true that B = C? Give a proof or provide a counterexample. 15. If Dn F= Dn G, is it necessarily true that F = G? Explain why or provide a counterexample. 16. Let U be the set of natural numbers 1 through 20, let A be the set of even numbers in U, and let B be the set of numbers in that are divisible by 3. (a) Find An B, AU B.AUB, and An B.
76 CHAPTER 2 Sets and Whole Numbers 11. Let G n n divides 90) and D listed form, G = (1,2,3,5,6. 9, 10, 15, 18, 30, 45,90) (nn divides 144). In (a) Find the listed form of the set D. (b) Find G n D (c) Which element of G nD is largest? 12. Draw and shade Venn diagrams that correspond to the following sets: (b) AU (BnC (d) AU (BnC) (f) An BnC (а) А ОВГС (c) (An B) UC (e) AUBUC 13. For each part, draw a Venn diagram whose loops for sets A, B. and C show that the conditions listed must hold. (a) AC C, B C C,AnB= (b) СС (АПВ) (c) (An B) CC 14. If A U B = AUC, is it necessarily true that B = C? Give a proof or provide a counterexample. 15. If Dn F= Dn G, is it necessarily true that F = G? Explain why or provide a counterexample. 16. Let U be the set of natural numbers 1 through 20, let A be the set of even numbers in U, and let B be the set of numbers in that are divisible by 3. (a) Find An B, AU B.AUB, and An B.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 4E
Related questions
Question
Number 14 please
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill