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.
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Transcribed Image Text: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.
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