Question

In: Advanced Math

discrete mathematics 1.  Show that if a | b and b | a, where a and...

discrete mathematics

1. 

Show that if a | b and b | a, where a and b are integers, then a = b or a = -b.  

//Ex. 5, Page 208.

2.

Show that if a, b, c, and d are integers such that a | c and b | d, then ab | cd.

//Ex. 6, Page 208. 

3.

What are the quotient and remainder when

a) 44 is divided by 8?

b) 777 is divided by 21?

f) 0 is divided by 17?

g) 1,234,567 is divided by 1001?   

//(a), (b), (f), and (g) Ex. 10, Page 209.

4.

Determine whether each of these integers is a prime.

a) 19

b) 27

e) 107

f) 113

//(a), (b), (e), and (f) Ex. 2, Page 217.

5.

Find the prime factorization of each of these integers.

a) 39

c) 101

d) 143

f) 899

//(a), (c), (d), and (f) Ex. 4, Page 217.

6.

What are the greatest common divisors of these pairs of integers?

a) 23 * 33 * 55 and 25 * 33 * 52

d) 22 * 7 and 53 * 13 

//(a) and (d) Ex. 20, Page 218.

7.

Find gcd(1000, 625) and lcm(1000, 625) and verify that gcd(1000, 625)*lcm(1000, 625) = 1000*625 

//Ex. 24, Page 218.

Solutions

Expert Solution


Related Solutions

Discrete Mathematics Find the number of subsets of S = {1, 2, 3, ... , 10}...
Discrete Mathematics Find the number of subsets of S = {1, 2, 3, ... , 10} that contain both 5 and 6. I know the answer is 2^8, however I have no idea how to go on to solve this problem.
CSC 231 Discrete Structures and Its Applications. (DISCRETE MATHEMATICS) (ONLY ANSWER IF YOU KNOW DISCRETE STRUCTURES....
CSC 231 Discrete Structures and Its Applications. (DISCRETE MATHEMATICS) (ONLY ANSWER IF YOU KNOW DISCRETE STRUCTURES. PLEASE DON'T GUESS) (This is GENERALIZED PERMUTATIONS AND COMBINATIONS) TO ANSWER THE QUESTION YOU HAVE TO FIRST FIGURE OUT IF IT'S 'r-permutations with repetition' or 'r-combinations with repetition' 1, How many PIN numbers of length 4 have at least one digit '9'? (hint: first find how many have a first digit '9', how many have a second digit '9',… then add it up.) 2....
Discrete Mathematics A tree contains 1 vertex of degree 2, 1 vertex of degree 3, 1...
Discrete Mathematics A tree contains 1 vertex of degree 2, 1 vertex of degree 3, 1 vertex of degree 4, 11 leaves and the remaining vertices have degree 3. Find the total number of vertices. Sketch two non-isomorphic trees statisfying the above mentioned conditions.
Discrete Mathematics Probability Worksheet Name __________________________________________ (1) Two ordinary dice are rolled. Find the probability that...
Discrete Mathematics Probability Worksheet Name __________________________________________ (1) Two ordinary dice are rolled. Find the probability that ... (a) ... the sum of the dice is 6, 7 or 8. (b) ... the sum of the dice is 5 or at least one of the dice shows a 5 .(c) ... the two dice match. (2) A card is drawn from an ordinary deck of 52 cards. Find the probability that the card is ... (a) ... an ace or a...
Hi , i want research about importance and applications of Discrete Structures (discrete mathematics) about 2-3...
Hi , i want research about importance and applications of Discrete Structures (discrete mathematics) about 2-3 word pages thanks
Discrete Math Course. On Z, let B be the set of subsets A of Z where...
Discrete Math Course. On Z, let B be the set of subsets A of Z where either A is finite or A complement is finite. Define + and * as union and interception. Show whether or not B is a boolean algebra.
[Discrete math] Show that it is possible to arrange the numbers 1, 2, . . ....
[Discrete math] Show that it is possible to arrange the numbers 1, 2, . . . , n in a row so that the average of any two of these numbers never appears between them. [Hint: Show that it suffices to prove this fact when n is a power of 2. Then use mathematical induction to prove the result when n is a power of 2.] I saw the solution but I don't understand why permutation pi is using here.....
The table below is a discrete probability distribution of study hours for mathematics in a given week.
The table below is a discrete probability distribution of study hours for mathematics in a given week.    Hours (x) 1 2 3 4 5 P(x) 0.16 0.22 ? 0.20 0.14 Find the probability of x=3. Find the mean and the standard deviation of this probability distribution. Find the probability that x is at most 4 hours.
A Discrete Mathematics professor has a class of students. Frustrated with their lack of discipline, he...
A Discrete Mathematics professor has a class of students. Frustrated with their lack of discipline, he decides to cancel class if fewer than some number of students are present when class starts. Arrival times go from on time (arrivalTime < 0) to arrival late (arrivalTime > 0).Given the arrival time of each student and a threshhold number of attendees, determine if the class is canceled. Input Format The first line of input contains t, the number of test cases. Each...
1. Show the steps in merging A and B into C where A= 8, 12, 19,...
1. Show the steps in merging A and B into C where A= 8, 12, 19, 34 B= 3, 5,15, 21
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT