(a) How many functions are there from a set with three elements to a set with five elements? Imagine creating a function from a 3-element set S to another set T as a three-step process. Step 1 sends the first element of S to an element in T; Step 2 sends the second element of S to an element in T; Step 3 sends the third eleme of S to an element in T. By the-Select- rule, the number of ways to create a function is the -Select--v of the number of ways to perform each of the three steps. So, the answer is (b) How many functions are there from a set with four elements to a set with two elements? (c) How many functions are there from a set with m elements to a set with n elements, where m and n are positive integers?

How many different functions are there from a set with 10 elements to sets with 2 elements?

let A be a set with n elements and B a set with m elements. How many different functions are there from A to B? Explain. If we assume n ≤ m, ho wmany one-to-one functions from A to B are there? Explain. If we assume n > m, how many one-to-one functions from A to B are there? Explain

True or False A function is a relation between two sets Dand R so that each element x in the first set D is related toexactly one element y in the second set R.

Let A = {a, b, c, d} and f = { (a, O), (c, 12), (d, 18), (b, 12) }. Is f a function %3D from A to B ? Yes, because each element in the range is paired with a unique element in the domain. O No, because 12 is paired with two domain values. O Yes, because each element in the domain is paired with a unique element in the range. No, because it doesn't pass the vertical line test.

4. Let W be the set of all words in the English language and let L be the set of letters {A, B, C,...,Z}. Let f: W→→L be the function that takes as input a word w and out- puts the first letter of the word. (a) Compute f({APPLE, CHERRY, STRAWBERRY}). (b) Give three elements in the set f-¹(P). (c) Is f a bijection? Use one or two sentences to explain your answer.

Determine whether f is a function from the set of all bit strings to the set of integers if a,b

6. Consider these functions from the set of students in a discrete mathematics class. Under what conditions is the function one-to-one if it assigns to a student his or her a) mobile phone number. b) student identification number. c) final grade in the class. d) home town

(1.) Let T = {1, 2, 3, 4, 5, 6, 7, 8, 9}.  Suppose five integers are chosen from T. Show that it is not true that there must be two integers whose sum is 10 by giving a counterexample. In other words, fill in the blank with five numbers from T, no two of which have a sum of 10. (Enter your answer in set-roster notation.) (2.) Suppose five pairs of similar-looking boots are thrown together in a pile. What is the minimum number of individual boots that you must pick to be sure of getting a matched pair? Why? Since there are 5 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be............? . It follows that if a minimum of............. boots is chosen, at least two must be from the same pair.

In the PMT function, what is not true about the type argument? Group of answer choices It is often filled in with zero. It is often left blank. It is required. It is optional.