Help with this problems please? 1. Give an example of a subset S of the set of all the subsets of N={a,b,c,d,e}, such that | S= 4and the partial order relation R on S, defined by c, is a total order on S.2. Suppose an airline has 7 pilots (A, B, C, D, E, F, G) and it serves 4 destinations (W, X, Y, Z).How many different assignments (one pilot per flight) are possible, if pilot A cannot fly to destination W,where one will get arrested.3. Suppose a universal set 2={0,1,2,..,9}. Give an example of sets A, B, and C, whereA-C = B-C, yet A±B.4. Simplify (A- B)O(B- A), where A and B are sets, subsets of a universal set N.5. Let S be the set of all the nonempty subsets of 2={a,b,c,d}.Define a relation R on S as follows: AR B if AOB±Ø.Is R an equivalence relation? Completelyjustify your answer.6. Let S be the set of the subsets of 2= {1,2, 3, 4} . Define a relation Ron S as follows:For X and Y in S : X RY means Xn{1,3} =Yn{1,3}. It is easy to see R is an equivalence relationon S- no need to verify that claim. Describe the equivalence classes of R by explicitly listing all theelements in each class. Note, the result of your work can be viewed as describing the partition Pof theset S, induced by the relation R.7. We are returning to the members of the Club from the last HWK. Suppose the management decidedto use, to rank the members, a relation R on the set of members, defined as follows:Let A and B be two members, then A R Bif either A belonged to the club at least as many years as B orA's contribution is at least as large as that of B.Is R, as defined above, a partial ordering? Explain.8. Let f:Z→Z be a function, mapping from the set of integers to the set of integers, defined asfollows f(n) = 3n +1. Is ƒ one-to-one? Is it onto?9. How many distinct functions mapping from set X= {a,b,c,d} onto set Y = {1,2} are there?

Name: Help with this problems please? 1. Give an example of a subset S of th
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Help with this problems please? 1. Give an example of a subset S of the set of all the subsets of N={a,b,c,d,e}, such that | S= 4and the partial order relation R on S, defined by c, is a total order on S.2. Suppose an airline has 7 pilots (A, B, C, D

As you asked more than one question I answered only first one.

Answered: 1. Give an example of a subset S of the…

Math

Advanced Math

1. Give an example of a subset S of the set of all the subsets of 2={a,b,c,d,e}, such that | S=4 and the partial order relation R on S, defined by C, is a total order on S.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 12E: 12. (See Exercise 10 and 11.) If each is identified with in prove that . (This means that the...

See similar textbooks

Related questions

Q: From the graph, determine the x- and y-intercepts and the vertical and horizontal asymptotes. (If an…

Q: Consider the initial value problem given below. -2+tsin(x). x(0)=0 Use the improved Euler's method…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: whale's dir

A: In the question we have to draw a graph on the position of the blue whale . AS PER OUR GUIDLINES…

Q: I need more help on this

A: Given information: μ=151000σ=35000 n=77

Q: Can you help me with Practice Problem, Thank you.

A: Step 1:

Q: I can't seem to understand the solution. Can someone write it down?

A: An inner city revitalization zone is a rectangle that is twice as long as it is wide. A diagonal…

Q: please explain how to solve this problem

A: *used power rule

Q: Can someone help me answer question 4 ?

A: Given that The number of classes (X) a student takes in a given semester follows the following…

Q: Find the average rate of change of g(r) = 5x - 1 from z - 2 to z = 1 =D1 =

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: (d) y = sin(tan(2r)) (e) f(t) = tan(eª) + etan(t) (f) y = ·

Q: Is it okay for you to write a detailed solution for this?

A: given curves y=2x2+10 , y=4x+16 , x=-2 and x=5 claim - Find the centroid of the region bounded by…

Q: i need worked out solution

A: Given integral,Formula used,The given integrand is not defined at . So, break the limits using the…

Q: Let S = {1,2, 3, ..., 18, 19, 20} be the universal set. Let sets A and B be subsets of S, where: Set…

A: Universal set: it the set of all elements of all related sets without any repetition. Subset: set of…

Topic Video

Question

Help with this problems please?

1. Give an example of a subset S of the set of all the subsets of N={a,b,c,d,e}, such that | S= 4
and the partial order relation R on S, defined by c, is a total order on S.
2. Suppose an airline has 7 pilots (A, B, C, D, E, F, G) and it serves 4 destinations (W, X, Y, Z).
How many different assignments (one pilot per flight) are possible, if pilot A cannot fly to destination W,
where one will get arrested.
3. Suppose a universal set 2={0,1,2,..,9}. Give an example of sets A, B, and C, where
A-C = B-C, yet A±B.
4. Simplify (A- B)O(B- A), where A and B are sets, subsets of a universal set N.
5. Let S be the set of all the nonempty subsets of 2={a,b,c,d}.
Define a relation R on S as follows: AR B if AOB±Ø.Is R an equivalence relation? Completely
justify your answer.
6. Let S be the set of the subsets of 2= {1,2, 3, 4} . Define a relation Ron S as follows:
For X and Y in S : X RY means Xn{1,3} =Yn{1,3}. It is easy to see R is an equivalence relation
on S- no need to verify that claim. Describe the equivalence classes of R by explicitly listing all the
elements in each class. Note, the result of your work can be viewed as describing the partition Pof the
set S, induced by the relation R.
7. We are returning to the members of the Club from the last HWK. Suppose the management decided
to use, to rank the members, a relation R on the set of members, defined as follows:
Let A and B be two members, then A R Bif either A belonged to the club at least as many years as B or
A's contribution is at least as large as that of B.
Is R, as defined above, a partial ordering? Explain.
8. Let f:Z→Z be a function, mapping from the set of integers to the set of integers, defined as
follows f(n) = 3n +1. Is ƒ one-to-one? Is it onto?
9. How many distinct functions mapping from set X= {a,b,c,d} onto set Y = {1,2} are there?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Research Design Formulation$

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.

Similar questions

Determine whether the set S={1,x2,2+x2} spans P2.
Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.
Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.
13. Consider the set of all nonempty subsets of . Determine whether the given relation on is reflexive, symmetric or transitive. Justify your answers. a. if and only if is subset of . b. if and only if is a proper subset of . c. if and only if and have the same number of elements.
In each of the following parts, a relation is defined on the set of all human beings. Determine whether the relation is reflective, symmetric, or transitive. Justify your answers. xRy if and only if x lives within 400 miles of y. xRy if and only if x is the father of y. xRy if and only if x is a first cousin of y. xRy if and only if x and y were born in the same year. xRy if and only if x and y have the same mother. xRy if and only if x and y have the same hair colour.
[Type here] 7. Let be the set of all ordered pairs of integers and . Equality, addition, and multiplication are defined as follows: if and only if and in , Given that is a ring, determine whether is commutative and whether has a unity. Justify your decisions. [Type here]
12. (See Exercise 10 and 11.) If each is identified with in prove that . (This means that the order relation defined in Exercise 10 coincides in with the original order relation in . We say that the ordering in is an extension of the ordering in .) 11. (See Exercise 10.) According to Definition 5.29, is defined in by if and only if . Show that if and only if . 10. An ordered field is an ordered integral domain that is also a field. In the quotient field of an ordered integral domain define by . Prove that is a set of positive elements for and hence, that is an ordered field. Definition 5.29 Greater than Let be an ordered integral domain with as the set of positive elements. The relation greater than, denoted by is defined on elements and of by if and only if . The symbol is read “greater than.” Similarly, is read “less than.” We define if and only if. As direct consequences of the definition, we have if and only if and if and only if . The three properties of in definition 5.28 translate at once into the following properties of in . If and then . If and then . For each one and only one of the following statements is true: . The other basic properties of are stated in the next theorem. We prove the first two and leave the proofs of the others as exercises.