1. List the elements of each of the following sets using roster notation: a. {x € Z* |- 5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1.
List the elements of each of the following sets using roster notation:
a. {x € Z* | – 5 <x < 5}
b. {x € Z |x? = 2}
2.
Describe each of the following sets using set builder notation:
а. {0,2, 4, 6, 8,...}
b. {..., -8, –7,–6,6,7,8, ...}
c. {0,10,20, 30, .. , 1000}
d. {2,3, 5, 7,11, 13}
3.
Find the power set of A = {1,{1}, Ø}.
Transcribed Image Text:1. List the elements of each of the following sets using roster notation: a. {x € Z* | – 5 <x < 5} b. {x € Z |x? = 2} 2. Describe each of the following sets using set builder notation: а. {0,2, 4, 6, 8,...} b. {..., -8, –7,–6,6,7,8, ...} c. {0,10,20, 30, .. , 1000} d. {2,3, 5, 7,11, 13} 3. Find the power set of A = {1,{1}, Ø}.
4.
Let A = {0,2,4, 6,8, 10}, B = {0,1,2, 3, 4, 5, 6}, and C = {4,5,6,7,8,9, 10}. Let the
universal set be the set of all integers. Find:
a. (AU B)nC
b. (An B)UC
с. (An B) -C
5.
Let A = {n E Z |n = 4i + 1 for some i e Z} and B = {m € Z |m = 4j – 3 for some je Z}.
Prove that A = B.
Hint: you must show that A C B and BC A. Remember to write down your proof in acceptable
mathematical language.
Transcribed Image Text:4. Let A = {0,2,4, 6,8, 10}, B = {0,1,2, 3, 4, 5, 6}, and C = {4,5,6,7,8,9, 10}. Let the universal set be the set of all integers. Find: a. (AU B)nC b. (An B)UC с. (An B) -C 5. Let A = {n E Z |n = 4i + 1 for some i e Z} and B = {m € Z |m = 4j – 3 for some je Z}. Prove that A = B. Hint: you must show that A C B and BC A. Remember to write down your proof in acceptable mathematical language.
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