Log in
HomeClass Notes1,200,000CA670,000

MATH135 Lecture Notes - Lecture 5: Empty Set, Asteroid Family, Cartesian Coordinate System

113 views2 pages
cerisegiraffe538
29 Sep 2015
School
University of Waterloo
Department
Mathematics
Course
MATH135
Professor
Shane Bauman

For unlimited access to Class Notes, a Class+ subscription is required.

leensy188 and 36637 others unlocked
MATH135 Full Course Notes
40
MATH135 Full Course Notes
Verified Note
40 documents

Document Summary

Math 135 - lecture 5: more divisibility and introduction to sets. Let a, b, and c be integers. If a | b and a | c then for any integers x and y, a | (bx + cy). Proof: assume m and 14 | and 14 | m, then 7 | (135m + 693) m. Since 14 | m, therefore 7 | m. Therefore 7 | (135m + 693) by dic. Objects that make up a set are called elements. Note: order in a set does not matter. A 3 does not belong to set a. A 2 belongs to set a, 3. We can represent a set in different ways: A complete list a = {2, 4, 6, 8} A list using b = {2, 4, 6, 8, ,100} = {,-3, -2, -1, 0, 1, 2, 3,} Using set-builder notation a = {x. The smallest possible set is the empty set:

Get access

Grade+
$40 USD/m
Billed monthly
Grade+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
10 Verified Answers
Class+
$30 USD/m
Billed monthly
Class+
Homework Help
Study Guides
Textbook Solutions
Class Notes
Textbook Notes
Booster Class
7 Verified Answers

Related textbook solutions

Calculus
4 Edition,
Rogawski
ISBN: 9781319050733
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
CALCULUS:EARLY TRANSCENDENTALS
4 Edition,
Rogawski
ISBN: 9781319050740

Related Documents

MATH135
Final Exam
Study Guide
MATH135 Final: Math 135 Final Notes
pinkbutterfly135
MATH135 Lecture Notes - Equivalence Class, Congruence (Geometry), Additive Inverse
MATH135 Lecture Notes - Lecture 7: Prime Number, Coprime Integers, Division Algorithm
azurechimpanzee251

Related Questions

1.Create a list that contains 10 successive integers starting with the value in the variable start. For example, if start is 7, the resulting list should be [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. Store the list in a variable named my_list. Assume that the value of start has already been set.
 
2.Create a list that is made up of the first half of the elements of a list called original_list. Store the new list in a variable called half_list. Assume that the original list has already been initialized and contains an even number of elements.
 
 
3. Write a predicate function called same_ends that accepts a list of integers and an integer (n) as arguments. Return True if the first n numbers in the list are the same as the last n numbers in the list, and False otherwise. For example, if the list was [1, 2, 3, 4, 99, 1, 2, 3, 4], the function would return True if n is 4 and False if n is 3. Assume that n is between 1 and the length of the list, inclusive.
 
4.Write a function called highest_values that accepts as arguments a list of numeric values and a single integer (n). The function should return a list made up of the largest n values from the argument list in order from lowest to highest. For example, if the argument list is [46, 82, 25, 61, 70, 33, 54] and n is 3, the return value should be [61, 70, 82]. Assume that the argument list contains at least n elements.
 
5.Assume that a list of integers stored in a variable named original contains exactly two elements that are zero. Write code that creates a separate list that contains the elements from original that are between the two zeros. Do not include the zeros in the new list. Store the list in a variable named between_zeros.
 
6. Write a function called price_range that accepts a list of floating-point numbers representing prices as an argument and returns the the difference between the highest price and the lowest price. Do NOT use the built-in functions max or min in your solution. Assume that all prices are positive values and that none of them exceed 10,000.00.
 
7. Write a function called count_vowels that accepts a string argument that represents a word and returns the number of vowels that are in the word. The vowels are A, E, I, O, and U (ignore the 'sometimes Y' rule). Count both uppercase and lowercase vowels.
 
8.
Assume that the variable table holds a two-dimensional list of integers. Write code that computes the sum of all elements in the table, assigning the result to the variable table_sum.

 

please solve all questions.

Show transcribed image text

  1. Given the following main program

    #main
    a = [5,2,9,6,3] doubleList(a) print a

    Implement the function named doubleList that takes one list argument and modifies the list so that each element in the list is doubled. The statement print(a) in the main program will then have to print [10,4,18,12,6]

  2. Given the following main program

    #main
    a = [5,2,9,6,3]
    b = reversedList(a) print b
    print a

    Implement the function named reversedList that takes one list argument and returns a list that contains the elements in the list argument in reverse order. The statement print(b) in the main program will then have to print [3,6,9,2,5]. The statement print(a) must print the original list [5,2,9,6,3] unaffected. This means your function should not modify the list argument.

  3. Given the following main program

    #main
    a = [5,2,9,6,3] reverseList(a) print a

    Implement the function named reverseList that takes one list argument and reverses the list so that the modified list contains the same elements in reverse order. The statement print(a) in the main program will then have to print [3,6,9,2,5]

  4. What is the return value of the functions doubleList, reversedList and reverseList in questions 1, 2, and 3 above?

  1. Given the following main program

    #main
    a = [5,2,9,6,3]
    b = evenElements(a) print b

    Implement the function named evenElements that takes one list argument and returns a list that contains the elements in the list argument that are even integers. The statement print(b) in the main program will then have to print [2,6]. What is the return value of the function? Your function should not modify the list argument.

  2. Given the following main program

    #main
    a = [5, 2, 9, 6, 3, 7, 19, 4, 8, 17, 21, 20, 15] removeOddElements(a)
    print a

    Implement the function named removeOddElements that takes one list argument and modifies the list so that all odd integers in the list are removed. The statement print(a) in the main program will then have to print [2,6,4,8,20]. What is the return value of the function?

  3. Part A
    #Main program A=[5,8,2,0,-5,3] n=-5
    answer = isFound(A, n) if answer == True:

    print "The integer is found in the list" else:

    print "The integer is not found in the list."

    Consider the main program shown above. Write a Python function named isFound that takes a list of integers and an integer as arguments and returns True if the integer is found in the list; otherwise it returns False.

    Remark: You are NOT allowed to use the in operator or any other built in function when you write this function. Instead, you must write a loop to go through the elements of the list.

    Part B

    Give the following main program

page2image58001280 page2image58001664

#main
A = [5,2,9,6,3]
B = [2,4,3,9,7,1,6,5]
flag = isList1InList2(A, B) if flag:

print "The list", A, "is contained in the list", B else:

print "The list", A, "is not contained in the list", B

Implement the function named isList1InList2 that takes two list arguments and returns True if and only if each element of the first list argument are found in the second list argument; otherwise it returns False.

Remark: You are NOT allowed to use the in operator or any other built in function when you write this function. Instead, if you wish, you can use the function you wrote in Part A.

For the lists shown in the main program, your function must return True because each element of list A is found in list B.

  1. A given List is known as Palindrome List if the reverse of the List contains the same elements in the same order of the original List. For example the List of integers [2, 5, 0, 3, 3, 0, 5, 2] is a Palindrome because the reverse of the List which is [2, 5, 0, 3, 3, 0, 5, 2] contains the same elements in the same order as the given List. However the List [1, 2, '2', 1] is not Palindrome because its reverse which is [1, '2', 2, 1] does not contain the same elements in the same order as the given List.

    Write a Python function named isPalindrome that takes a List as argument and returns True if the argument is a Palindrome List; otherwise it returns False. You don't need to write the main program; just write the function. If you would like to test your function, then it is ok to write the main program too but you will not get any mark for the main program.

  2. Given your function in question #7 above, what is the output of the following code: a=[]

    b = [5,2,9,6,3]

    print isList1InList2(a,b)

  3. Given your function in question #7 above, what is the output of the following code:

    a=[]
    b=[]
    print isList1InList2(a,b)

  4. Given your function in question #7 above, what is the output of the following code: a = [5,2,9,6,3]

    b=[]

print isList1InList2(a,b)

  1. Given the following main program

    #main
    a=[]
    n = readListElements(a)
    print "The user entered", n, "elements to the list" print a

    Implement the function named readListElements that takes one list argument and modifies the list by repeatedly asking the user to enter integer values and then appending them to the list. The process stops when the user enters -1000. The stopping value -1000 should not be appended to the list. Moreover your function must count the appended elements and return it. Example if the user enters the integers 31, -4, 9, 1,-1000 then your function must modify the list a to a = [31, -4, 9, 1] and return the number elements added which is 4.

  2. Write a function named createRandomList that takes an integer argument n and returns a list with n elements. The elements must be random numbers in the range [0,100]

  3. Given the following main program:

    #main

       n = int(input("How many elements do you want in your list? "))
   a = createList(n)
   s1 = sumOfElementsAtEvenIndexes(a)
   print s1

       s2 = sumOfElementsAtOddIndexes(a)
   print s2
   s3 = sumOfAllElements1(a)
   print s3

       s4 = sumOfEvenElements(a)
   print s4
   s5 = sumOfOddElements(a)
   print s5

       s6 = sumOfAllElements2(a)
   print s6
   if (s3 != s6):

             print "Something is wrong in your program."
   else:

             print "Looks like you have done a good job."

    Implement the functions as follows:

  •  createList: returns a list object with n elements. The elements are generated randomly so that each element is in the range [15,45]

  • sumOfElementsAtEvenIndexes: returns the sum of the elements at even indexes. Use a for loop or a while loop.

  • sumOfElementsAtOddIndexes: returns the sum of the elements at odd indexes. Use a for loop or a while loop.

  • sumOfAllElements_A: returns the sum of all the elements in the list using the functionssumOfElementsAtEvenIndexes and sumOfElementsAtOddIndexes. Here you are NOT allowed to use any loop; instead make function calls as described.

  • sumOfEvenElements: returns the sum of the even integer elements in the list. Use a for loop or a while loop.

  • sumOfOddElements: returns the sum of the odd integer elements in the list. Use a for loop or a while loop.

  • sumOfAllElementsB: returns the sum of all the elements in the list using the functions sumOfEvenElements and sumOfOddElements. Here you are NOT allowed to use any loop; instead make function calls as described.

17. Most data compression algorithms like winzip, gzip, lzip and etc are based on the frequency distribution of characters in a given string. Write a function named getFreqDistribution that takes a string argument and returns a LIST that has length 26 such that the first element of the list is the number of appearance of 'a' or 'A' in the string, the second element is number of appearance of 'b' or 'B', and so on so forth.

I'm studying python 2 and have a lot of troubles with solving these homework questions.