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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 element of s to an element in t. by the ---select--- rule, the number of ways to create a function is the ---select--- 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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BhavikaKukreja

Functions are there from a set with three elements to a set with five elements:

What is element?

Element is a substance that cannot be broken down into any other substance by chemical means. It is made up of only one type of atom. Elements are the fundamental building blocks of all matter, and are the basis of all chemical compounds. Elements are divided into four categories: metals, nonmetals, metalloids, and noble gases. Each element has its own unique properties, such as its atomic number, atomic mass, and chemical properties, which are determined by the number of protons, neutrons, and electrons the element contains.

(a) Product,

(b) 4,

(c) m^n. The number of functions from a set with m elements to a set with n elements is equal to the number of ways to assign each element of the m-element set to an element of the n-element set, which is m^n.

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