Question: Show that if is an integer and n + 5 is odd, then n is even. f n is ode n = 2 k+1

Show that if " is an integer and n + 5 is odd, then n is even. f n is ode n = 2 k+1 13 + 5 = ( 215+ 1 ) = ( 2 k +1 ) 3 AS = ( 2 k + 1 ) ( 2k+1 ) ( 2 k+ 1 ) +5 = ( 4 1 2 + 2 k + 2k + 1 ) ( 21 + 1 ) +5 = ( 4 k 2 + 4 K + 1 ) ( 2 k +1 ) +5 = ( 8 k 3 + 4 k 2 + 8 k 2 + 9 k + 2k+1 ) +s = ( 81

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock 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!

Problem 2: Consider the set of integers. 1. Use a direct proof to show that the sum of two odd integers is even. 2. Use a direct proof to show that the product of two odd integers is odd. 3. Prove...

Problem #4 (20 points) a) Give a direct proof to show that if x is an even integer, then x+x is an even integer. b) Show that if n is an integer and n +5 is odd, then n is even using a proof by...

only the blue ,,, discete mathematics TAB TABLE 1 Rules of Inference. Rule of Inference Tautology Name Ide (PA(-9) Modus ponens AL (Apq)) Modus tollens AC AL An ((p - )^( g r) (p) Hypothetical...

o Show that if n is an integer and n +5 is odd, then n is even using: - b) a proof by contradiction

Section 8.3 Reading Assignment: Trigonometric Integrals Instructions. Read through this assignment and complete the three exercises below by reading the appropriate passages of the textbook. This...

Create the entire truth table for this statement. p^ (qVr) 2. (10 POINTS) Create the entire truth table for this statement. (p^g) V (p^r) 3. (2 POINTS) Refer to your answers to Problems 1 and 2 to...

Section 8.3 Reading Assignment: Trigonometric Integrals Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three questions very...

Consider the following statement The product of any even integer and any odd integer is even (a) Suppose the given statement is rewritten in the form, V integers m and n, if (hypothesis) then...

A first year co-op student working for Solutia Inc. recorded the transactions for the month. He wasnt exactly sure how to journalize and post, but he did the best he could. He had a few questions,...

Hugret Ltd is a company operating in the hotel industry and it owns two hotels, both operating as separate investment centre. The financial information of both hotels over the last four years is...

If an employer fails to file payroll tax reports, the firm will be penalized at a rate of _ _ _ _ _ _ _ _ _ blank per month. Multiple Choice 2 % 1 5 % 1 0 % 5 %

Net present values for three alternative investment projects follow. (a) If the company accepts all positive net present value investments, which of these projects will it accept? (b) If the company...