Provide the proofs for Theorem 7.2(a), and (b). Theorem 7.2 Given a set A with |A| =

Question:

Provide the proofs for Theorem 7.2(a), and (b).
Theorem 7.2
Given a set A with |A| = n and a relation R on A, let M denote the relation matrix for R. Then
(a) R is reflexive if and only if In ≤ M.
(b) R is symmetric if and only if M = Mtr.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Discrete and Combinatorial Mathematics An Applied Introduction

ISBN: 978-0201726343

5th edition

Authors: Ralph P. Grimaldi

See More Books

Question Posted: Jun 21, 2016 08:31 AM

See More Questions

Provide the proofs for the remaining parts of Theorems 6.1 and 6.2.
Complete the proofs for Corollary 10.1 and parts (b) and (c) of Theorem 10.2. Corollary 10.1 Let a,b, c Z+ with b 2, and let f: Z+ R. If f(1) = c, and f(n)=af(n/b) + c, for n=bk, k 1, then (1) f ...
Provide the details of the proof of Theorem 9.38. u(to) E (ker K= rngK
In Exercises 5 and 6, the transition matrix P for a Markov chain with states 0 and 1 is given. Assume that in each case the chain starts in state 0 at time n = 0. Find the probability that the chain...
The manager of the Excom Service Station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has...
A fluorescent lamp manufacturer guarantees that the mean life of a certain type of lamp is at least 10,000 hours. You want to test this guarantee. To do so, you record the lives of a random sample of...
Air flows isentropically through a duct as shown in Fig. P11.37. For the conditions shown, find the Mach number at both stations 1 and 2 and the flow rate. The diameter is not necessarily constant....
Valpaige Company is an industrial machinery and equipment manufacturer with several production departments. The company employs automated and heavy equipment in its production departments....
A metallic sphere of diameter 5 cm is initially at a uniform temperature of 300oC. Suddenly the metal sphere is immersed in a fluid at 30oC. The convective heat transfer coefficient between the...
Haltoyb Chicken Sdn Bhd was established in year 2015 as a poultry business. The business operation focuses on supplying and producing processed chicken to the northern region market of the Peninsular...
Let A be a set with |A| = n, and consider the order for the listing of its elements as fixed. For R A A, let M (R) denote the corresponding relation matrix. (a) Prove that M (R) = 0 (the n n...
Use Theorem 7.2 to write a computer program (or to develop an algorithm) for the recognition of equivalence relations on a finite set. Theorem 7.2 Given a set A with |A| = n and a relation R on A,...
Calculate the standard entropy change for the following reactions at 25C. Comment on the sign of r S. (a) 2 Al(s) + 3 Cl 2 (g) 2 AlCl 3 (s) (b) 2 CH 3 OH() + 3 O 2 (g) 2 CO 2 (g) + 4 H 2 O(g)
An investor concerned whether a company can meet its near-term obligations is most likely to calculate the: A. current ratio. B. return on total capital. C. financial leverage ratio.
If the outcome of a long-term contract can be measured reliably, the preferred accounting method under both IFRS and US GAAP is: A. the cost recovery method. B. the completed contract method. C. the...
Debt due within one year is considered: A. current. B. preferred. C. convertible.
Distinguishing between current and non-current items on the balance sheet and presenting a subtotal for current assets and liabilities is referred to as: A. a classified balance sheet. B. an...
Denali Limited, a manufacturing company, had the following income statement information: Denalis gross profit is equal to A. $280,000. B. $500,000. C. $1,000,000. Revenue Cost of goods sold Other...
Bravo Manufacturing Company is negotiating with a customer for the lease of a large machine manufactured by Bravo. The machine has a cash price of $800,000. Bravo wants to be reimbursed for financing...
The domain of the variable in the expression x 3/x + 4 is________.
Elizabeth is a landscape designer. She created a small pond with a fountain that her company plans to manufacture and market. It is a free-form shape and the company wants to include the area of the...
Interpret the quote in the contest of your own home?
Allison has a mortgage with, North End Bank. The bank requires that she pay her homeowner's insurance, property taxes, and mortgage in one monthly payment. Her monthly mortgage payment is $1,390, her...
A cylindrical log is cut as shown to form a park bench. Find: a. The area of triangle OAB in m. [2] b. The volume of the log in m. [3] B 70% 40 cm 3m
Security issues in today's workplace. Identify the different types of potential security issues an employer may have to deal with. Give examples to illustrate each of these potential security...
Research on the Internet and identify an emerging security issue. Describe the issue and its origin. Provide an example of this new security issue. Discuss the impacts of the security issue and...

Provide the proofs for Theorem 7.2(a), and (b). Theorem 7.2 Given a set A with |A| =

Question:

Step by Step Answer:

a R reflexive x x R for all x A m ...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Linear Algebra questions