Write your own example of a set P containing 5 ordered pairs (x, y) such that P is not a function.
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Write your own example of a set P containing 5 ordered pairs (x, y) such that P is not a function.
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- Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. Bag union and intersection are defined in terms of #. bag-union: List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-union. bag-intersection : List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-intersection. Allowed functions. Your code must use only the following functions:1. define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. +, -, /, * No loops or use of hash Racket code only please.…Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. Bag union and intersection are defined in terms of #. bag-union: List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-union. bag-intersection : List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-intersection. Allowed functions. Your code must use only the following functions:1. define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. +, -, /, * Racket code only please. Thank you!Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. sum : List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing the list resulting from simply appending the input lists together. Racket code only please. No loops Allowed: 1. define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond7. +, -, /, * Thank you!
- Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. sum : List × List -> List This function should take as arguments two lists representing bags and should return the list representing the list resulting from simply appending the input lists together. Racket code only please. No loops Allowed: 1. define, let2. lambda, curry3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. map, append-map, andmap, ormap, filter, apply7. +, -, /, * Thank you!Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. Bag union and intersection are defined in terms of #. bag-union: List × List -> List This function should take as arguments two lists representing bags and should return the list representing their bag-union. bag-intersection : List × List -> List This function should take as arguments two lists representing bags and should return the list representing their bag-intersection. Allowed functions. Your code must use only the following functions:1. define, let2. lambda, curry3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. map, append-map, andmap, ormap, filter, apply7. +, -,…Consider the function f= {(n,n² – 1) such that n<5,n€N}, written in set-builder notation, which defines a set containing a list of ordered pairs. Write the inverse of f as a set in list form containing ordered pairs. O fl={(0,1),(3,2),(8,3),(15,4)} O fl={(0,– 1),(1,0), (2,3),(3,8),(4,15)} ofl={(1,0), (2,3),(3,8),(4,15)} O fl= {(-1,0),(0,1),(3,2),(8,3),(15,4)} o fl={(3,2),(8,3),(15,4)}
- Implement a general use function that determines if one set exactly contains a square transform of the other set Input parameter 1 - A set collection of integer values Input parameter 2 - A set collection of integer values Return Value - Boolean - Is every element in one set the square of every element in the other set? EXAMPLE: { 1, 2, 3, 4, 5 } and { 1, 4, 9, 16, 25 } returns TRUE EXAMPLE: { 1, 4, 9, 16, 25 } and { 1, 2, 3, 4, 5 } returns TRUE EXAMPLE: { 1, 4, 9 } and { 1, 2, 3 } returns TRUE EXAMPLE: { 1, 4, 9, 22 } and { 1, 2, 3, 7 } returns FALSE since 7*7 is not 22 EXAMPLE: { 1, 4, 9, 16, 25, 36, 49 } and { 1, 2, 3, 4, 5, 6 } returns FALSE since the number of elements in both sets is not the same In C++ Programming code onlyIf F is a function and dom(F) is a set, then F is a set.Hint. Prove first that ran(F) is a setWrite a python program to implement the different set operation Union, Intersection, Difference and Symmetric for the set. E= {A, B, Z, J, F} N= {B, H, I, F, A}
- Define a function compress : lists(T) → lists(T) that accepts a list argument (of some generic type T) and returns a list without any subsequent redundancies, e.g. compress(⟨a, a, b, b, b, c, c, a, b⟩) = ⟨a, b, c, a, b⟩ 1. Transform the definition into a computable function.2. Define f recursively.3. Unfold your definition for compress(⟨a, a, b, b, c, a⟩).4. (PROGRAMMING) Please map your definition into a Common LISP function. Place your code in file compress.lisp. The code should behave as follows: > (compress ’(a a a b c d d e))(A B C D E)> (compress ’())NIL> (compress ’(a b c c c a))(A B C A)> (compress ’(a a b b c c c c a b b))(A B C A B)Write up what the properties of sets, lists, vectors and strings are and whether they are mutable or immutable. Then consider the class of problems that they are best for and use some code to illustrate your points. E.g., if you have a function that solves a problem using lists, then you can say why you can/can’t use vectors for it or sets etc?Write a function in c programming language that gets an array of points ( function is defined as : typedef struct{ int x; Int y; } point; ) and sorts the array using qsort().Given two points a=(ax,ay) and b=(bx,by) we compare them as follows: 1) if (ax)2+(ay)2 < (bx)2+(by)2, then a should come before b in the sorted array. 2) if (ax)2+(ay)2 = (bx)2+(by)2, then we compare the points by the x coordinate. Remark: For a point a=(ax,ay) the quantity ((ax)2+(ay)2)1⁄2 is the distance of a from the (0,0). That is, we sort the points according to their distance to (0,0), and if for points at the same distance, then we sort them according to the first coordinate. You will need to implement the comparison function, and apply qsort() on the array with this comparison function. For example: - Input: [(3,2), (7,1), (1,1), (3,4), (5,0), (7,1)] - Expected output: [(1,1), (3,2), (3,4), (5,0), (7,1), (7,1) ] Explanation:(1,1) is first because 12+12=2 is the smallest(3,2)…
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