Question: 39. Proof: Suppose r and s are rational numbers. If r +s is rational 39. Proof: Supposer and s are rational numbers. If r +

39. "Proof: Suppose r and s are rational numbers. If r +s is rational

39. Proof: Suppose r and s are rational numbers. If r s is rational, then by definition of rational r + s = a/b for some integers a and b with b 0, Also since r and s are rational, r = i/j and s = m/n for some integers i, j, m, and n with j?0 and n O. It follows that n a n b which is a quotient of two integers with a nonzero denomi- nator. Hence it is a rational number. This is what was to be shown.

39. "Proof: Supposer and s are rational numbers. If r + s is rational, then by definition of rational r + s = a/b for some integers a and b with b 0. Also sincer and s are rational, r = i/j and s= m/n for some integers i, j, m, and n with j #0 and n = 0. It follows that i m r+s=+ 'b' which is a quotient of two integers with a nonzero denomi- nator. Hence it is a rational number. This is what was to be shown."

Step by Step Solution

★★★★★

3.53 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Since Q the field of rational numbers is closed under usual addition ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Show that if R and S are both n-ary relations, then Pi1,i2,...,im(R S) = Pi1,i2,...,im(R) Pi1,i2,...,im(S).

Q:

Let A = {R, S| R and S are regular expressions and L(R) L(S)}. Show that A is decidable.

Q:

39. "Proof: Supposer and s are rational numbers. If r + s is rational, then by definition of rational r + s = a/b for some integers a and b with b 0. Also sincer and s are rational, r = i/j and s=...

Q:

Patients who undergo chronic hemodialysis often experience severe anxiety. Videotapes of progressive relaxation exercises were shown to one group of patients and neutral videotapes to another group....

Q:

In 2013, France's labor unions won a case against Sephora to prevent the retailer from staying open late, and forcing its workers to work "antisocial hours." The cosmetics store does about 20% of its...

Q:

Tobacco and Alcohol in Childrens Movies Refer to Data Set 13 Alcohol and Tobacco in Movies in Appendix B and use the times (seconds) that animated Disney movies showed the use of tobacco and the...

Q:

Using the Benign Breast Disease data set and the appropriate confidence interval formula, compute a 95% confidence interval for the mean weight of (a) the case group (???? = 50). (b) the control...

Q:

Sally wants to purchase a Burger Barn franchise. She can buy one for $ 750,000. Burger Barn headquarters provides the following information: Estimated annual cash revenues $ 420,000 Typical annual...

Q:

help Problem 2-19 (Algo) Multiple Predetermined Overhead Rates; Applying Overhead [LO2-1, LO2-2, LO2-4] High Desert Potteryworks makes a variety of pottery products that it sells to tetailers. The...

Q:

The data set cherry.dat, from Hand et al. (1994), contains measurements of diameter (inches), height (feet), and timber volume (cubic feet) for a sample of 31 black cherry trees. Diameter and height...

Q:

If a project costs $72,000 and returns $18,500 per year for 5 years, what is its IRR? A) 8.98% B) 8.50% C) 7.39% D) 7.67%

Q:

the Continuous Loop Model (paper posted in Modules), consider how or if this approach might be used to improve a value stream or project where you work or an organization you know well. How could you...

Q:

Market research is vital to sustainable export success in analysing international markets. It is a process that can help you avoid costly expansion mistakes and identify extraordinary business...

Q:

To learn more about the role of a supervisor, you will interview someone in a supervisory position; your selection cannot be yourself or someone in the class. Identify someone you think is an...

Q:

Draw a labelled diagram of the Dicot stem.

Q:

The magnitude and direction of two forces acting on an object are 50 pounds, S73E, and 110 pounds, N71E, respectively. Find the magnitude, to the nearest hundredth of a pound, and the direction...

Q:

Select the correct option. Evaluate ((2)/(3))^(3). 8

Q:

Find the radius of convergence in two ways: (a) Directly by the CauchyHadamard formula in Sec. 15.2. (b) From a series of simpler terms by using Theorem 3 or Theorem 4.

Q:

Let A = {R| R is a regular expression describing a language containing at least one string w that has 111 as a substring (i.e., w = x111y for some x and y)}. Show that A is decidable.

Q:

Let = {0,1}. a. Let A = {0 k u0 k | k 1 and u * }. Show that A is regular. b. Let B = {0 k 1u0 k | k 1 and u * }. Show that B is not regular.

Q:

Define UPATH to be the counterpart of PATH for undirected graphs. Show that BIPARTITE L UPATH. (Note: In fact, we can prove UPATH L, and therefore BIPARTITE L, but the algorithm [62] is too...

Q:

According to the Employee Benefit Research Institute (www.ebri.org) 34% of workers between the ages of 35 and 44 owned a 401(k)-type retirement plan. Suppose a recent survey was conducted by the...

Q:

Most major airlines allow passengers to carry two pieces of luggage (of a certain maximum size) onto the plane. However, their studies show that the more carry-on baggage passengers have, the longer...

Q:

The Federal Communications Commission released a report (Leslie Cauley, USA Today, Study: A la Carte Cable Would Be Cheaper, February 10, 2006) refuting an earlier report released in 2004 by the...

Related Book

Introduction to the theory of computation 3rd edition by Michael Sipser