8. A student writes the following for the function f(x) = - Br+8 " The domain of f(x) is (-2, -4) U (-4, t)“ Is this correct? If not, what is the correct domain of f(x) ?
8. A student writes the following for the function f(x) = - Br+8 " The domain of f(x) is (-2, -4) U (-4, t)“ Is this correct? If not, what is the correct domain of f(x) ?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me solve 8-12. Thanks
![CSE230 (Discrete Mathematics)
Assignment 1
Topics: Set, Function and Combinatorics
Set:
1. Write the expression in set builder notation. Also provide the number line.
(-10,3] N [-5, 5)
2. A = {1, 3,5} B= {red, green}
Find out the power sets of set A and B. Also write down the cartesian product of A and B.
What's the cardinality of this cartesian product?
3. Use set builder notation to establish the first De Morgan law
A' n B' = (A U B)'
4. A travel group has 105 travelers. Of them, 50 travelers already visited India, 30 Nepal, 20
Bhutan, 6 both India and Nepal, I both India and Bhutan, 5 Nepal and Bhutan, and one of them
visited all the 3 countries.
Mirza Md. Tanjim shorif Mug.
7:02 PM Yesterday
Function:
Determine the number of travelers that
5. Is the relation given by the following set of ordered pairs a function?
{(1.2), (5,6). (8, 6). (7.2), (9.2), (8,6) }. Explain your reasoning.
did not visit any of these countries.
6. For f(x) = cos(4x - 1), find the range of f(x). What should be the domain of f(x)?
7. Find the domain of f(x) = log (x* - 3)
8. A student writes the following for the function f(x) =
8x+8
" The domain of f(x) is (-x0, -4) U (-4, +e) "
Is this correct? If not, what is the correct domain of f(x) ?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93cd9a1d-4aef-4349-8452-e90cf27dc453%2F8f0efc74-0ea0-47d8-bdcd-d12b87cec005%2Fhz1hk7k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:CSE230 (Discrete Mathematics)
Assignment 1
Topics: Set, Function and Combinatorics
Set:
1. Write the expression in set builder notation. Also provide the number line.
(-10,3] N [-5, 5)
2. A = {1, 3,5} B= {red, green}
Find out the power sets of set A and B. Also write down the cartesian product of A and B.
What's the cardinality of this cartesian product?
3. Use set builder notation to establish the first De Morgan law
A' n B' = (A U B)'
4. A travel group has 105 travelers. Of them, 50 travelers already visited India, 30 Nepal, 20
Bhutan, 6 both India and Nepal, I both India and Bhutan, 5 Nepal and Bhutan, and one of them
visited all the 3 countries.
Mirza Md. Tanjim shorif Mug.
7:02 PM Yesterday
Function:
Determine the number of travelers that
5. Is the relation given by the following set of ordered pairs a function?
{(1.2), (5,6). (8, 6). (7.2), (9.2), (8,6) }. Explain your reasoning.
did not visit any of these countries.
6. For f(x) = cos(4x - 1), find the range of f(x). What should be the domain of f(x)?
7. Find the domain of f(x) = log (x* - 3)
8. A student writes the following for the function f(x) =
8x+8
" The domain of f(x) is (-x0, -4) U (-4, +e) "
Is this correct? If not, what is the correct domain of f(x) ?
![Combinatorics:
9. Three young brother-sister pairs from different families need to take a trip in a van. These six
children will occupy the second and third rows in the van, each of which has three seats. To
avoid disruptions, the siblings may not sit right next to each other in a row and no child may sit
directly in front of his or her sibling. How many seating arrangements are possible for this trip?
10. Every positive integer greater than 1 has at least two divisors and can be written as a unique
product of some prime number/s with exponents. For example,
5 = 5'has two divisors (1 and 5 itself)
6 = 2' x 3' has four divisors (1, 2, 3 and 6)
16 = 2° has five divisors (1, 2, 4, 8 and 16).
a,
If a number n = p," x P x P, x x PX Pwhere p, Py P3 P-r P,are prime
numbers and a,, a, a, ar a,are the corresponding exponents of the prime numbers, how
X ...X
many divisors does n have?
11. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?
12. [Bonus] In how many ways can 7 people A, B, C, D, E, F and G be seated at a round table so
that no two of A, B and C sit next to each other?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93cd9a1d-4aef-4349-8452-e90cf27dc453%2F8f0efc74-0ea0-47d8-bdcd-d12b87cec005%2Fjy9t9vg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Combinatorics:
9. Three young brother-sister pairs from different families need to take a trip in a van. These six
children will occupy the second and third rows in the van, each of which has three seats. To
avoid disruptions, the siblings may not sit right next to each other in a row and no child may sit
directly in front of his or her sibling. How many seating arrangements are possible for this trip?
10. Every positive integer greater than 1 has at least two divisors and can be written as a unique
product of some prime number/s with exponents. For example,
5 = 5'has two divisors (1 and 5 itself)
6 = 2' x 3' has four divisors (1, 2, 3 and 6)
16 = 2° has five divisors (1, 2, 4, 8 and 16).
a,
If a number n = p," x P x P, x x PX Pwhere p, Py P3 P-r P,are prime
numbers and a,, a, a, ar a,are the corresponding exponents of the prime numbers, how
X ...X
many divisors does n have?
11. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?
12. [Bonus] In how many ways can 7 people A, B, C, D, E, F and G be seated at a round table so
that no two of A, B and C sit next to each other?
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