Question: Show that these statements about the real number x are equivalent: (i) x is irrational, (ii) 3x + 2 is irrational, (iii) x/2 is irrational.

Show that these statements about the real number x are equivalent: (i) x is irrational, (ii) 3x + 2 is irrational, (iii) x/2 is irrational.

Step by Step Solution

★★★★★

3.48 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

It is easiest to give proofs by contraposition of i ii ii i i iii and iii i For the f... 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

Document Format (1 attachment)

Word file Icon

923-M-C-M-S (1358).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

The following compound was isolated from nerve cells. (a) Describe how this compound differs in structure from fats and oils. (b) Three products are obtained when this compound is hydrolyzed with...

Q:

Show that these statements about the integer x are equivalent: (i) 3x + 2 is even, (ii) x + 5 is odd, (iii) x2 is even.

Q:

Show that these statements are inconsistent: "If Miranda does not take a course in discrete mathematics, then she will not graduate." "If Miranda does not graduate, then she is not qualified for the...

Q:

Show that each of these statements can be used to express the fact that there is a unique element x such that P(x) is true. a) xy(P(y) x = y) b) xP(x) xy(P(x) P(y) x = y) c) x(P(x) y(P(y) x =...

Q:

Show that these statements about the real number x are equivalent: ( i ) x is irrational, ( ii ) 3 x + 2 is irrational, ( iii ) x 2 is irrational. Please show all work and explain the steps; thank...

Q:

Please answer ALL questions or none at all. Thank you in advance. Use direct proof to show that: a) If n is an even integer, then n2 is an even integer. b) The product of two odd numbers is odd. Give...

Q:

81) Given f(x) = 3x5 + 2x4 - 8, find f(-2). 88) Determine an equation of a polynomial function of lowest degree whose zeros are 1, 2, and -1. A) f(x) = x3 - 2x2 -x -2 B) f(x ) = x3 - 2x2 - x - 2 C) f...

Q:

Math Project Pick out the 4 or (arguably) 5 theorems that would be best proved using Mathematical Induction. Rewrite theorems 1 and 6 as conditional statements. Describe the strategy required to...

Q:

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

Q:

# 7 (chapter 5)(40 points, Due on Friday November 11) Question 1. [3 points each] Use the definition of Limit of functions to prove that x2 2 . 5 5 2 lim x 3 x 1 1 (B) x 1 (A) lim x 0 if x 2 2x (C)...

Q:

1) Find all real solutions of: 4 2 2 x + x =3 2 x 4 + x23=0 4 2 2 2 x 2 x +3 x 3=0 x ( 21)=0 2 x 2 ( x 21)+ 3 ( 2 x2 +3 ) ( x 21 ) =0 ( 2 x2 +3 ) =0 2 2 x =3 3 x 2= 2 3 x= 2 3 x= i 2 2) Given the...

Q:

What is the effect on the NPV of the restructured transaction in the preceding problem if Firm Hs marginal tax rate in year 2 increases to 42 percent?

Q:

A plane is being tracked by radar, and data is taken every second in polar coordinates and r. At 206 seconds, use the centered finite difference (second-order correct) to find the vector expressions...

Q:

For many years the concentrated holdings by large block holders made hostile takeovers in Europe more difficult to complete. Group of answer choices True False

Q:

Compute a simple index for the revenue of GE using the period 201314 as the base. What can you conclude about the change in revenue over the period? General Electric Employees (thousands) Revenue...

Q:

For the unity feedback system shown in Figure 8.3, where do the following: a. Sketch the root locus. b. Find the value of K that will yield a 10% overshoot. c. Locate all nondominant poles. What can...

Q:

GF is a company that manufactures clothes for the fashion industry.The fashion industry is fast moving and consumer demand can change quickly due to the emergence of new trends.GF manufactures three...

Q:

Show how to calculate the number of iterations of a general Fortran 90- style do loop. Your code should be written in an assembler-like notation, and should be guaranteed to work for all valid bounds...

Q:

Suppose that the consumers preferences are given by the utility function U(C, l) = ln C + ln l,where > 0. Determine the consumers choice of consumption and leisure and interpret your solutions.

Q:

A bearing assembly contains 10 bearings. The bearing diameters are assumed to be independent and normally distributed with a mean of 1.5 millimeters and a standard deviation of 0.025 millimeter. What...

Q:

Suppose that in Example 2.4.2 we ignored the ages of the children and distinguished only three family types: (boy, boy), (girl, boy), and (girl, girl). Would the conditional probability of both...

Q:

An eyes-only diplomatic message is to be transmitted as a binary code of 0s and 1s. Past experience with the equipment being used suggests that if a 0 is sent, it will be (correctly) received as a 0...

Q:

When Zach wants to contact his girlfriend and he knows she is not at home, he is twice as likely to send her an e-mail as he is to leave a message on her answering machine. The probability that she...

Q:

Question 18 Builtrite stock is currently selling for $40 and recently paid a dividend of $2.00. The stock has a projected constant growth rate of 10%. If you purchase this stock, what is your...

Q:

Grady Home Health has a profit margin of 15 percent on sales of $20 million. If the firm has debt of $7.5 million and total assets of $22.5 million, what is Grady's return on assets? 13.3 percent...

Q:

Maynard, Inc. has no debt outstanding and a total market value of $250,000. Earnings before interest and taxes, EBIT, are projected to be $28,000 if economic conditions are normal. If there is strong...