Let R1, R2 be relations on a set A. (a) Prove or disprove that R1, R2 reflexive

Question:

Let R1, R2 be relations on a set A.
(a) Prove or disprove that R1, R2 reflexive ⇒ R1 ⋂ R2 reflexive,
(b) Answer part (a) when each occurrence of "reflexive" is replaced by
(i) Symmetric;
(ii) Antisymmetric; and
(iii) Transitive.

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

Answer Exercise 7, replacing each occurrence of by . Exercise 7 Let R1, R2 be relations on a set A. (a) Prove or disprove that R1, R2 reflexive R1 R2 reflexive, (b) Answer part (a) when each...
For each of the following statements about relations on a set A, where |A| = n, determine whether the statement is true or false. If it is false, give a counterexample. (a) If R is a relation on A...
For a set A, let R1 and R2 be symmetric relations on A. If R1 o R2 R2 o R1, prove that R1 o R2 = R2 o R1.
In Exercises 1 through 22, find the critical points of the given functions and classify each as a relative maximum, a relative minimum, or a saddle point. f(x, y) = x 4 32x + y 3 12y + 7
Develop a seasonally adjusted forecast for the demand data for fertilizer in Problem 12-3. Use a linear trend line model to compute a forecast estimate for demand in year 4.
Fill in the Blank. In the wave-solution $w(x, t)=w_{1}(x-c t)+w_{2}(x+c t)$, the first term represents the wave that propagates in the __________ directions of $x$. conditions
What are the five phases in the project management life cycle?
In early January 2011, Reymont Corporation applied for a trade name, incurring legal costs of $18,000. In January 2012, Reymont incurred $7,800 of legal fees in a successful defense of its trade...
if current ratio increases and quick ratio decreases what is most likely going on ?
Mr. Gopal furnishes the following data related to the manufacturing of a product during the month of April 2004. Raw .Materials ConsumedDirect Labour Charges Machine Hou$ Worked Machine Hour Rate...
For each of the following relations, determine whether the relation is reflexive, symmetric, antisymmetric, or transitive. (a) R Z+ Z+ where a R b if a|b (read "a divides b," as defined in Section...
For A = {1, 2, 3, 4}, let R and S be the relations on A defined by R = {(1, 2), (1, 3), (2, 4), (4, 4)} and S = {(1, 1), (1, 2), (1, 3), (2, 3), (2, 4)}. Find R o S, S o R, R2, R3, and S2.
Blue Spruce is a large wholesale gardening operation that sells trees, shrubs, and a variety of perennials and other bedding plants to small retail garden shops throughout New England. The company is...
An ideal gas expands adiabatically and quasistatically in a chamber fitted with a piston. Is this process isothermal, isentropic, isobaric, isochoric, or none of these?
Devil's Throat, the longest drop in Iguazu Falls on the Brazil-Argentina border, has a height of $82 \mathrm{~m}$. If all the kinetic energy a given volume of water acquires in dropping through...
A helium atom is in a nanowire (a wire with a diameter on the scale of molecules) in thermal equilibrium at $77 \mathrm{~K}$. (a) The atom is constrained in the nanowire and so can move in only one...
A beam of white light has the same intensity at all visible-light wavelengths. Does the beam contain more red-light photons or more blue-light photons?
A diatomic molecule in thermal cquilibrium at $120 \mathrm{~K}$ is constrained to move freely only on a two-dimensional surface. (a) What is the molecule's thermal energy? (b) The molecule is...
Find the derivative of the function. y= y = S/ - - dt
Describe a job you have had in the past or a job you are very familiar with. Indicate the negative aspects of the job and how it could be improved with current human resource management techniques.
Identify the error(s) on Rorie's W-2 from below. a Employee's social security number 000-00-0000 Safe, accurate, -e file Visit the IRS website at www.irs.gov/efle. OMB No. 1545-0008 FAST! Use b...
How can the quote the interpreted in light of what you have learned?
a. Determine the correlation coefficient and linear regression equation that expresses the square footage as a function of the monthly rent. Round the numbers in the equation to the nearest...
Suppose Stocks A, B and C are the only three component stocks in a benchmark index. The number of shares outstanding of Stocks A, B and C are 369,000 shares, 327,000 shares, and 240,000 shares,...
Botanists have determined that some species of weed grow in a circular pattern. For one such species, the area A , in square meters, can be approximated by A ( t ) = 0.004 t 2 , where t is the time...
Book Print ciences Gallatin Carpet Cleaning is a small, family-owned business operating out of Bozeman, Montana. For its services, the company has always charged a flat fee per hundred square feet of...

Let R1, R2 be relations on a set A. (a) Prove or disprove that R1, R2 reflexive

Question:

Step by Step Answer:

a For all x A x x R 1 R 2 so x x R 1 R 2 and R 1 R 2 is reflexiv...View the full answer

Discrete and Combinatorial Mathematics An Applied Introduction

Students also viewed these Linear Algebra questions