given the definition:
A partially ordered set S is said to be "inductive" if every chain
of S has an upper bound in S.
Show that (1) and (2) are equivalent.
Homework Answers
Answer:
Partially Ordered Set:
A partially ordered set S is a pair, (X,<=)
of a set X whose elements are called the elements or
vertices of S and an order relation 
which obeys the following
rules:
Reflexivity: a <= a for all X
Anti-symmetry: a <= b and b <= a if and only if a = b
Transitivity: if a <= b and b <= c then a <= c.
Maximal Element:
In a poset an element is not related to any other element, then it is called maximal element.
Add Answer to:
given the definition: A partially ordered set S is said to be "inductive" if every chain...
(10 pt) For a partially ordered set (S,
See picture
(10 pt) For a partially ordered set (S, <) a "least element" is an element a e S for which a x for all x e S. In other words, a is "less than or equal to" all elements in the set In contrast, a "minimal element" is an element m € S for which·m → x m for all x E S. In other words, no element in the set is "less than or equal to" m...
Recall that (a,b)⊆R means an open interval on the real number line: (a,b)={x∈R|a<x<b}. Let ≤ be...
Recall that (a,b)⊆R means an open interval on the real number line: (a,b)={x∈R|a<x<b}. Let ≤ be the usual “less than or equal to” total order on the set A=(−2,0)∪(0,2). Consider the subset B={−1/n | n∈N,n≥1}⊆A. Determine an upper bound for B in A.. Then formally prove that B has no least upper bound in A by arguing that every element of A fails the criteria in the definition of least upper bound. Note: make sure you are addressing the technical...
plz use the definition solve the question Definition 1. Given a set A CR, an elementu...
plz use the definition solve the question
Definition 1. Given a set A CR, an elementu ER is an interior point of A if there exists an e > 0 such that (x - 5,3 +E) CA. The interior of A is the set Aº consisting of all interior points of A. A set A is called open if A= A'. Definition 2. Given a set A CR, an element X ER is a limit point of A if for...
5- Recall that a set KCR is said to be compact if every open cover for...
5- Recall that a set KCR is said to be compact if every open cover for K has a finite subcover 5-1) Use the above definition to prove that if A and B are two compact subsets of R then AUB is compact induction to show that a finite union of compact subsets of R is compact. 5-2) Now use 5-3) Let A be a nonempty finite subset of R. Prove that A is compact 5-4) Give an example of...
PROBLEM e Definition: A GROUP is a set S paired with an operation *, denoted <S,*>...
PROBLEM e
Definition: A GROUP is a set S paired with an operation *,
denoted <S,*> satisfying the four properties;
G0: CLOSURE - For any a, b in S, a * b in S
G1: ASSOCIATIVITY - For all a, b, c in S, (a * b) * c = a * (b
* c)
G2: IDENITY - There exists an element e in S such that a * e =
e = b * a, for all a in...
PLEASE ANSWER THE FOLLOWING IN C++!! PLEASE READ THE QUESTION CAREFULLY!!! AS WELL AS WHOEVER ANSWERS...
PLEASE ANSWER THE FOLLOWING IN
C++!! PLEASE READ THE QUESTION CAREFULLY!!! AS WELL AS WHOEVER
ANSWERS THIS CORRECTLY I WILL UPVOTE!!!
In this project you will design, implement and test the ADT set using both Arrays and Linked Lists and implement all the operations described in the following definitions in addition to the add and remove operations. Sets are one of the basic building blocks for the types of objects considered in discrete mathematics. A set is an unordered collection...
Question 8 Let R be relation on a set A. 1. When is R said to...
Question 8
Let R be relation on a set A. 1. When is R said to be an equivalence relation? Give a precise definition, using appropriate quantifiers etc. 2. When is R said to be an partial order? Give a precise definition, using appropriate quantifiers etc (You don't need to redefine things that you defined in the previous part... you may simply mention them to save time.) 3. On Z, define a relation: a D biff a - b is...
Please prove the following theorems using the provided axioms and definitions, using terms like s...
Please prove the following
theorems using the provided axioms and definitions, using terms
like suppose, let..ect. Please WRITE CLEARLY AND TYPE IF YOU
CAN.
1 Order Properties Undefined Terms: The word "point" and the expression "the point x precedes the point y" will not be defined. This undefined expression will be written x 〈 y. Its negation, "x does not precede y," will be written X y. There is a set of all points, called the universal set, which is...
Let S be the set of binary strings defined recursively as follows: Basis step: 0ES Recursive step...
discrete math. Structural Induction: Please write and
explain clearly. Thank you.
Let S be the set of binary strings defined recursively as follows: Basis step: 0ES Recursive step: If r ES then 1rl E S and 0x0ES (I#x and y are binary strings then ry is the concatenation of and y. For instance, if 011 and y 101, then ry 011101.) (a) List the elements of S produced by te first 2 applications of the recursive definition. Find So, Si...
Let X be a finite set and F a family of subsets of X such that...
Let X be a finite set and F a family of subsets of X such that every element of X appears in at least one subset in F. We say that a subset C of F is a set cover for X if X =U SEC S (that is, the union of the sets in C is X). The cardinality of a set cover C is the number of elements in C. (Note that an element of C is a...
See picture
(10 pt) For a partially ordered set (S, <) a "least element" is an element a e S for which a x for all x e S. In other words, a is "less than or equal to" all elements in the set In contrast, a "minimal element" is an element m € S for which·m → x m for all x E S. In other words, no element in the set is "less than or equal to" m...
plz use the definition solve the question
Definition 1. Given a set A CR, an elementu ER is an interior point of A if there exists an e > 0 such that (x - 5,3 +E) CA. The interior of A is the set Aº consisting of all interior points of A. A set A is called open if A= A'. Definition 2. Given a set A CR, an element X ER is a limit point of A if for...
5- Recall that a set KCR is said to be compact if every open cover for K has a finite subcover 5-1) Use the above definition to prove that if A and B are two compact subsets of R then AUB is compact induction to show that a finite union of compact subsets of R is compact. 5-2) Now use 5-3) Let A be a nonempty finite subset of R. Prove that A is compact 5-4) Give an example of...
PROBLEM e
Definition: A GROUP is a set S paired with an operation *,
denoted <S,*> satisfying the four properties;
G0: CLOSURE - For any a, b in S, a * b in S
G1: ASSOCIATIVITY - For all a, b, c in S, (a * b) * c = a * (b
* c)
G2: IDENITY - There exists an element e in S such that a * e =
e = b * a, for all a in...
PLEASE ANSWER THE FOLLOWING IN
C++!! PLEASE READ THE QUESTION CAREFULLY!!! AS WELL AS WHOEVER
ANSWERS THIS CORRECTLY I WILL UPVOTE!!!
In this project you will design, implement and test the ADT set using both Arrays and Linked Lists and implement all the operations described in the following definitions in addition to the add and remove operations. Sets are one of the basic building blocks for the types of objects considered in discrete mathematics. A set is an unordered collection...
Question 8
Let R be relation on a set A. 1. When is R said to be an equivalence relation? Give a precise definition, using appropriate quantifiers etc. 2. When is R said to be an partial order? Give a precise definition, using appropriate quantifiers etc (You don't need to redefine things that you defined in the previous part... you may simply mention them to save time.) 3. On Z, define a relation: a D biff a - b is...
Please prove the following
theorems using the provided axioms and definitions, using terms
like suppose, let..ect. Please WRITE CLEARLY AND TYPE IF YOU
CAN.
1 Order Properties Undefined Terms: The word "point" and the expression "the point x precedes the point y" will not be defined. This undefined expression will be written x 〈 y. Its negation, "x does not precede y," will be written X y. There is a set of all points, called the universal set, which is...
discrete math. Structural Induction: Please write and
explain clearly. Thank you.
Let S be the set of binary strings defined recursively as follows: Basis step: 0ES Recursive step: If r ES then 1rl E S and 0x0ES (I#x and y are binary strings then ry is the concatenation of and y. For instance, if 011 and y 101, then ry 011101.) (a) List the elements of S produced by te first 2 applications of the recursive definition. Find So, Si...
Most questions answered within 3 hours.
-
(Problem 1d). Leandro has 16 hours per day that he can allocate
to work or leisure....
asked 10 minutes ago -
Morganton Company
makes one product and it provided the following information to help
prepare the master...
asked 35 minutes ago -
2Al + 3Cl2 --> 2AlCl3
If one mole Al is reacted w two moles Cl2, how...
asked 1 hour ago -
1. You will see some trends in the movement of each currency vs.
the US Dollar....
asked 1 hour ago -
9. (9 pts) An investor with a stock portfolio worth several
hundred thousand dollars sued his...
asked 1 hour ago -
Which statement is true?
a. Unless directed otherwise, the computer automatically
executes C. statements one before...
asked 2 hours ago -
When a new company is considering Speed to Market for a product
launch, which would provide...
asked 2 hours ago -
bacteria and their metabolites could either promote or protect from
cancer. Explain one of these cases...
asked 2 hours ago -
Use the sample data and confidence level given below to complete
parts (a) through (d).
A...
asked 3 hours ago -
During laser vision correction, a brief burst of 193 nm
ultraviolet light is projected onto the...
asked 3 hours ago -
1 ) How well does the initial speed, v0,calculated from Equation
4 agree with the value...
asked 3 hours ago -
1. What is the p-value for a right tail test for a single
proportion with a...
asked 4 hours ago