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(a) What is the number of onto functions f : {1,2, 3, 4, 5} → {1,2, 3}? (b) What is the number of one to one functions f : {1,2,3} → {1,2, 3, 4, 5}?

(a) What is the number of onto functions f : {1,2, 3, 4, 5} → {1,2, 3}? (b) What is the number of one to one functions f : {1,2,3} → {1,2, 3, 4, 5}?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Transcription for Educational Website Consider the following questions related to functions and mappings between sets: (a) **What is the number of onto functions \( f : \{1, 2, 3, 4, 5\} \to \{1, 2, 3\}?** An onto function, also known as a surjective function, is one where every element in the codomain (the set \{1, 2, 3\} in this case) is mapped by at least one element from the domain (the set \{1, 2, 3, 4, 5\}). (b) **What is the number of one-to-one functions \( f : \{1, 2, 3\} \to \{1, 2, 3, 4, 5\}?** A one-to-one function, also known as an injective function, is one where no two elements of the domain map to the same element in the codomain. Here, each element in the domain \{1, 2, 3\} maps to a unique element in the codomain \{1, 2, 3, 4, 5\}.
Transcribed Image Text:### Transcription for Educational Website Consider the following questions related to functions and mappings between sets: (a) **What is the number of onto functions \( f : \{1, 2, 3, 4, 5\} \to \{1, 2, 3\}?** An onto function, also known as a surjective function, is one where every element in the codomain (the set \{1, 2, 3\} in this case) is mapped by at least one element from the domain (the set \{1, 2, 3, 4, 5\}). (b) **What is the number of one-to-one functions \( f : \{1, 2, 3\} \to \{1, 2, 3, 4, 5\}?** A one-to-one function, also known as an injective function, is one where no two elements of the domain map to the same element in the codomain. Here, each element in the domain \{1, 2, 3\} maps to a unique element in the codomain \{1, 2, 3, 4, 5\}.
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