(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?
(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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:(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?
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