39. Proof: Supposer and s are rational numbers. If r + s is rational, then by...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
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." 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."
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
39. "Proof: Suppose r and s are rational numbers. If r +s is rational 39. "Proof: Supposer and s are rational numbers. If r + s is rational, then by definition of rational r + s = a/b for some...
-
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).
-
Let A = {R, S| R and S are regular expressions and L(R) L(S)}. Show that A is decidable.
-
A sample of size n is randomly selected from a non-normal population with mean and standard deviation o. a. Describe the mean and standard deviation of the sampling distribution of X for all samples...
-
Remember Earl, who sells lemonade in Philadelphia? You met him in the chapter on cost functions. Earls production function is f(x1, x2) = x1/3 1 x21/3, where x1 is the number of pounds of lemons he...
-
Identify the compounds from Exercise 10.7 that provide the most pronounced example of the following chemical characteristics and give a balanced equation that illustrates each of the characteristics:...
-
The Collapsible Chair Company Limited was incorporated in 1972 and traded profitably until the 1990 s. During the early 1990 s the entry of new competitors into the market led to a fall in demand for...
-
VaultOnWheels Corporation operates a fleet of armored cars that make scheduled pickups and deliveries for its customers in the Phoenix area. The company is implementing an activity-based costing...
-
I need help on an assignment on power series, taylor series, and fourier series! Appreciate it if you may show me how to. 1 Power Series - practice Determine the largest open interval on which each...
-
A pharmaceutical company produces a sinus medicine. Monthly sales (in thousands of doses) for the past three years are shown in the table on the next page. a. Develop a regression model that allows...
-
Social Identity Theory and Social Identity Performance: How has learning and understanding these concepts changed you or influenced some aspect of your life? -provide an example or two for each...
-
Task 1: Interference of waves 1. Using the two-dimensional wave interference pattern shown, a ruler and the two equations involving wave path difference, complete the following. 1. Measure the...
-
Discuss what teamwork means to you in any work environment. Discuss two situations in which teamwork promote the above statement in any healthcare setting.
-
Exercise 8-52 (Algo) Prepare a Production Cost Report: FIFO Method (LO 8-2, 4, 5, 6) Beverly Plastics produces a part used in precision machining. The part is produced in two departments: Mixing and...
-
GoodGro Inc. makes genetically modified seeds that are identical to Harvest Corporation's patented seeds, without Harvest's permission. This is most likely trademark infringement. patent...
-
what is relative to accounting?
-
Consider the curve given by x^2 = 5xy - 6. At time t = 2, the value of x is 3 and dx/dt at t=2 is -5. Find dy/dt at t=2.
-
An auto-parts manufacturer is considering establishing an engineering computing center. This center will be equipped with three engineering workstations each of which would cost $25,000 and have a...
-
Define the function majority n as in Problem 9.24. Show that it may be computed with O(n) size circuits. Problem 9.24. Recall that you may consider circuits that output strings over {0,1} by...
-
Let 3 contains all size 3 columns of 0s and 1s. A string of symbols in 3 gives three rows of 0s and 1s. Consider each row to be a binary number and let B = {w * 3 | the bottom row of w is the sum...
-
Let f : N N be any function where f(n) = o(n log n). Show that TIME(f(n)) contains only the regular languages.
-
Compute weighted-average contribution margin (Learning Objective 4) Use the information from the Bay Cruiseline Data Set. Suppose Bay Cruiseline decides to offer two types of dinner cruises: regular...
-
Changes in fixed costs (Learning Objective 3)} Use the information from the Bay Cruiseline Data Set. Suppose Bay Cruiseline embarks on a cost-reduction drive and slashes fixed expenses from \(\$...
-
Compute and use operating leverage factor (Learning Objective 5) Use the information from the Bay Cruiseline Data Set. a. Compute the operating leverage factor when Bay Cruiseline sells 10,000 dinner...
Study smarter with the SolutionInn App