D. List five different natural numbers that are congruent to 8 modulo 6. E. List five different natural numbers that are congruent to 10 modulo 4. F. Determine the day of the following dates using Modular Arithmetic: 1) August 11, 1982 2) October 9, 2002 3) January 17, 2006 4) December 30, 2008 A. Evaluate each of the following, where O and e indicate addition and subtraction,respectively, on a 12-hour clock.1) 305 =2) 804 =3) 6 0 10 =4) 509 =5) 10 011 =11)6 0 10 =12)5 O 9 =Section Break(Continuous) -6) 11 é 5 =_7) 10 e 6 = -8) 7011 =9) 5e 10 =10)4 e9 =13)7 e 11 =14)5 e 10 =,B. (Military Time) Evaluate each of the following, where e and e indicate additionand subtraction, respectively, on a 24-hour clock. -- Section Break(Continuous)--1) 1800A 09002) 0800A 09003) 1600A 12004) 1300A 13005) 1000A 14006) 1200A 07007) 1800A 19008) 0200.9) 0900,10)0600050018002200-C. Determine whether the congruence is true or false.1) 7 = 12 mod 52) 15 =1 mod 83) 5 = 8 mod 34) 21 = 45 mod 65) 5 = 20 mod 4Section Break(Continuous)6) 88 = 5 mod 97) 11 = 15 mod 48) 18 = 60 mod 79) 72 = 30 mod 510)25 = 85 mod 12D. List five different natural numbers that are congruent to 8 modulo 6.E. List five different natural numbers that are congruent to 10 modulo 4.F. Determine the day of the following dates using Modular Arithmetic:1) August 11, 19822) October 9, 20023) January 17, 20064) December 30, 2008

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List five different natural numbers that are congruent to 8 modulo 6.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.7: Introduction To Coding Theory (optional)

Problem 18E

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Question

D. List five different natural numbers that are congruent to 8 modulo 6.

E. List five different natural numbers that are congruent to 10 modulo 4.

F. Determine the day of the following dates using Modular Arithmetic:

1) August 11, 1982

2) October 9, 2002

3) January 17, 2006

4) December 30, 2008

A. Evaluate each of the following, where O and e indicate addition and subtraction,
respectively, on a 12-hour clock.
1) 305 =
2) 804 =
3) 6 0 10 =
4) 509 =
5) 10 011 =
11)6 0 10 =
12)5 O 9 =
Section Break(Continuous) -
6) 11 é 5 =_
7) 10 e 6 = -
8) 7011 =
9) 5e 10 =
10)4 e9 =
13)7 e 11 =
14)5 e 10 =,
B. (Military Time) Evaluate each of the following, where e and e indicate addition
and subtraction, respectively, on a 24-hour clock. -- Section Break(Continuous)--
1) 1800A 0900
2) 0800A 0900
3) 1600A 1200
4) 1300A 1300
5) 1000A 1400
6) 1200A 0700
7) 1800A 1900
8) 0200.
9) 0900,
10)0600
0500
1800
2200-
C. Determine whether the congruence is true or false.
1) 7 = 12 mod 5
2) 15 =1 mod 8
3) 5 = 8 mod 3
4) 21 = 45 mod 6
5) 5 = 20 mod 4
Section Break(Continuous)
6) 88 = 5 mod 9
7) 11 = 15 mod 4
8) 18 = 60 mod 7
9) 72 = 30 mod 5
10)25 = 85 mod 12
D. List five different natural numbers that are congruent to 8 modulo 6.
E. List five different natural numbers that are congruent to 10 modulo 4.
F. Determine the day of the following dates using Modular Arithmetic:
1) August 11, 1982
2) October 9, 2002
3) January 17, 2006
4) December 30, 2008

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