In: Advanced Math

Determine if the binary relation <= is a partial order on A in the following cases:

(a) A = N × N and (a1, b1) (a2, b2) ⇔ a1 <= a2 for (a1, b1),(a2, b2) ∈ A

(b) X = {1, 2, 3, 4}, A = P(X) and a <= b ⇔ #a <= #b for a, b ∈ A (Here #a denotes the number of elements in the set a)

(c) A = N and a <= b ⇔ ∃k ∈ N : a^k = b

What does it mean for a relation is a partial order
relation?

Problem 4.9.4 (10) In Section 2.10 we proved that every
partial order is the “path-below” relation of a graph called
a Hasse diagram. How does the Hasse diagram relate to
the graph of the partial order itself? Present the proof of
the Hasse Diagram Theorem using mathematical induction.

Determine whether or not the following is an equivalence
relation on N. If it is not, determine which property fails. If it
is, prove it.
(a) x ∼ y if and only if x|y (x evenly divides y).
(b) x ∼ y if and only if the least prime dividing x is the
same as the least prime dividing y. In this case, instead if using
N, use the set A = {2,3,4,5,...}.
(c) x∼yifandonlyif|x−y|<5.
(d) x∼yifandonlyifx=4.
2. Prove that...

In a case-control study, cases and controls are compared in order
to determine whether they differ with respect to their exposure
levels.
true or false?

Determine taxable income in each of the following independent
cases. In all cases, the company was very profitable in all years
prior to 2017 and it had retained earnings of $1,000,000 at the end
of 2017.
In 2018, Company A has taxable income of $60,000 prior to
consideration of any net operating loss. In 2017, the Company
incurred a net operating loss of $10,000. They did not elect to
waive the carryback period. Determine 2018 taxable income.
In 2018, Company...

Show that, for each of the following fields, it is impossible to
define an order relation ≤ that would make it an ordered field: (a)
The set {0, 1} with addition and multiplication modulo 2. (b) The
field of complex numbers.

Create a Binary Search Tree for the following data and do
In-order, Preorder and Post-order traversal of the tree.
50, 60, 25, 40, 30, 70, 35, 10, 55, 65, 5
Write an algorithm to delete a node in Singly Linked
List
[12
Write an algorithm of Binary
Search
[10]
Write a program in ‘C’ to generate Fibonacci series using
recursion
[8]

For each of the following determine whether ∗ is a binary
operation on R. If so, determine whether or not ∗ is associative,
commutative, has an identity element, and has inverse elements.
(a) a ∗ b = (ab) / (a+b+1)
(b) a ∗ b = a + b + k where k ∈ Z
(c) a ln(b) on {x ∈ R | x > 0}

Determine the taxable Capital Gains in the following cases separately :(a) Ms. Sehajpreet purchased a house on 1-5-1995 for Rs. 4,60,000. She sold the house on 10-6-2017 (CII : 272) for Rs. 20 lakhs. On 14-7-2017, she purchased another house at Chandigarh for Rs. 4 lakhs. She did not own any other house property.(b) Mr. Kulbir sold a plot on July 10, 2017 (CII : 272) for Rs. 6,05,000; Cost of acquisition on June 15 , 2007 (CII: 129 ) was Rs....

For the following cases, determine the ratio of the fugacity in
the final state to that in the initial state for steam undergoing
the isothermal change of state:
a) From 9000 kPa and 673.15 K to 300 kPa
b) From 7000 kPa and 700 K to 345 kPa

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- Annuity You are going to borrow money from the bank. But when considering your income, you...
- As you will learn, working in groups is no easy task! Hopefully, you will master some...
- An agronomist is conducting a field experiment to identify the best management practice for minimizing spread...
- What’s a firm’s market value? What are some factors driving a firm’s market value?
- Create the following positions based upon a job analysis: Mailroom clerk: Entry level for a long-term...
- Discuss the events that lead to the crime control model. Explain how community corrections and evidence-based...
- In 2018, Chevelle Company has sales of $39,500, cost of $18,400, and depreciation of $1,900 and...

ADVERTISEMENT