 # MAT 214 Discrete Mathematics: Homework 4 questions Anonymous
timer Asked: Feb 19th, 2019
account_balance_wallet \$5

### Question Description

do the home work Discrete Mathematics (MAT 214) Homework 4 Complete the following problems on a separate sheet of paper. Write as much as possible for full credit, including calculator work. This assignment is due on Friday, February 22nd . Prove the following statements: 1) If a is any odd integer and b is any even integer, then 2a + 3b is even. 2) If n is any odd integer, then (−1)n = −1. 3) For all integers m, if m > 3 then m2 − 4 is composite. 4) For all integers n and m, if n − m is even then n3 − m3 is even. 5) The following three proofs are connected. The main result is to show that given two rational numbers, you can find another rational number between the two of them. This will be part c. Use the results from a and b to show this. a) If r and s are any two rational numbers, then r+s 2 b) For all real numbers a and b, if a < b then a < ties of inequalities in T17-T27 of Appendix A.) is rational. a+b 2 < b. (You may use the proper- c) Given any two rational numbers r and s with r < s, there is another rational number between r and s. You should use the results from parts a and b to show this.

mikewinter3
School: Duke University   Attached.

1

Discrete Mathematics: Homework 4

Student name:
Institutional affiliation:

2
Discrete Mathematics: Homework 4
The attached word document addresses the question “Discrete Mathematics 5 questions” by
Complete the following problems on a separate sheet of paper. Write as much as possible for full
credit, including calculator work. This assignment is due on Friday, February 22nd .
Prove the following statements:
1.

If a is any odd integer and b is any even integer, then 2a + 3b is even.

2.

If n is any odd integer, then (−1)n = −1.

3.

For all integers m, if m > 3 then m2 − 4 is composite.

4. For all integers n and m, if n − m is even then n 3 − m3 is even.
5. The following three proofs are connected. The main result is to show that given two rational

numbers, you can find another rational number between the two of them. This will be part
c. Use the results from a and b to show this.
a. If r and s are any two rational numbers, then r+s 2 is rational.
b. For all real numbers a and b, if a < b then a < (a+b)/2 < b. (You may use the properties

of inequalities in T17-T27 of Appendix A.)
c. Given any two rational numbers r and s with r < s, there is another rational number

between r and s. You should use the results from parts a and b to show this.

1

Running Head: Discrete Mathematics: Homework...

flag Report DMCA  Review Anonymous
awesome work thanks Brown University

1271 Tutors California Institute of Technology

2131 Tutors Carnegie Mellon University

982 Tutors Columbia University

1256 Tutors Dartmouth University

2113 Tutors Emory University

2279 Tutors Harvard University

599 Tutors Massachusetts Institute of Technology

2319 Tutors New York University

1645 Tutors Notre Dam University

1911 Tutors Oklahoma University

2122 Tutors Pennsylvania State University

932 Tutors Princeton University

1211 Tutors Stanford University

983 Tutors University of California

1282 Tutors Oxford University

123 Tutors Yale University

2325 Tutors