1. Determine whether the first is a subset of the second, the second is a subs neither is a subset of the other. a. The set of people who were born in the U.S., the set of people who : b. The set of students studying a programming language, the set of
1. Determine whether the first is a subset of the second, the second is a subs neither is a subset of the other. a. The set of people who were born in the U.S., the set of people who : b. The set of students studying a programming language, the set of
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:b. {a,b}
c. {Ø, {Ø}}
6. How many elements does each of these sets have where a and b are distinct elements?
а. Р(а, b, (а, b}})
b. Р(Ф,а, (а}, {{а}}})
с. Р(Р(0))
{0, 1}. Find
7. Let A = {a, b, c}, B = {x, y}, and C =
а. АхВх С
b. СхВxА
с. СхАх В
8. Translate each of these quantifications into English and determine its truth value.
a. Vx E R (x² # -1)
b. Эх € Z (x2 %3D2)
с. Уx€ Z (x2 > 0)
d. 3x € R (x² = x)
9. 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}. Find
a. A n B n c
b. A U BU C
с. (A U B) ОС
d. (A n B) U C
10. Let A, B, and C be sets. Use the identities to show that
(A U B) n (B U C) n (Ā U C) = Ān ĒnT.
![Instructions:
> You need to turn in the assignment via Canvas.
> It is recommended to provide the solutions in a word document or a PDF. You will get the
practice to type related equations that will help you in the exams where you will also require
to type the solutions.
> You may also solve the assignment on paper (handwritten) and scan it to make one PDF file
for submission.
1. Determine whether the first is a subset of the second, the second is a subset of the first, or
neither is a subset of the other.
The set of people who were born in the U.S., the set of people who are U.S. citizens.
b. The set of students studying a programming language, the set of students studying
Java.
The set of animals living in the ocean, the set of fish.
а.
C.
2. For each of these intervals, list all its elements.
а. [а, а]
b. [а, а)
с. (а, а]
d. (a, a)
3. For each of the following sets, determine whether 2 is an element of that set.
a. {x E R| x is an integer greater than 1}
b. {x € R|x is the square of an integer}
с. {2,(2}}
d. {{2}, {{2}}}
е. {{2}, (2, (2}}}
f. {{2}}}
4. Determine whether each of these statements is true or false.
a. x E {x}
b. {x} C {x}
с. {x} € {x}
d. {x} € {{x}}
e. Ø C {x}
f. Ø E {x}
5. Find the power set of each of these sets, where a and b are distinct elements.
a. {a}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F891f4b43-b58e-440c-9713-3029294b2f55%2F8421adfa-0440-41ba-b904-0c8ee140449b%2Fr6h02y6_processed.png&w=3840&q=75)
Transcribed Image Text:Instructions:
> You need to turn in the assignment via Canvas.
> It is recommended to provide the solutions in a word document or a PDF. You will get the
practice to type related equations that will help you in the exams where you will also require
to type the solutions.
> You may also solve the assignment on paper (handwritten) and scan it to make one PDF file
for submission.
1. Determine whether the first is a subset of the second, the second is a subset of the first, or
neither is a subset of the other.
The set of people who were born in the U.S., the set of people who are U.S. citizens.
b. The set of students studying a programming language, the set of students studying
Java.
The set of animals living in the ocean, the set of fish.
а.
C.
2. For each of these intervals, list all its elements.
а. [а, а]
b. [а, а)
с. (а, а]
d. (a, a)
3. For each of the following sets, determine whether 2 is an element of that set.
a. {x E R| x is an integer greater than 1}
b. {x € R|x is the square of an integer}
с. {2,(2}}
d. {{2}, {{2}}}
е. {{2}, (2, (2}}}
f. {{2}}}
4. Determine whether each of these statements is true or false.
a. x E {x}
b. {x} C {x}
с. {x} € {x}
d. {x} € {{x}}
e. Ø C {x}
f. Ø E {x}
5. Find the power set of each of these sets, where a and b are distinct elements.
a. {a}
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