Find the number of onto function between two sets A={1,2,3,4} and B={4,5,6}

Name: Problem 103, Chapter 1: Differential Calculus Booster with Problems and Solutions for JEE Main and Advanced
Uploaded: 2022-02-28T15:00:09-08:00
Duration: 2 min 12 s
Channel: Sahil Kumar
Description: Find the number of onto function between two sets A={1,2,3,4} and B={4,5,6}

step 1 Hi guys, so we have this problem in which we need to find out total number of onto function The

Find the number of onto function between two sets...

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Key Concepts

Onto Functions

Onto functions, also called surjective functions, are functions in which every element in the codomain has at least one preimage in the domain. This means that the function covers the entire codomain. When counting onto functions, the challenge is ensuring that all elements of the codomain are 'hit' by the mapping, which typically requires careful combinatorial analysis.

Inclusion-Exclusion Principle

The inclusion-exclusion principle is a fundamental combinatorial technique used to determine the count of elements in a union of sets by subtracting the over-counted sections. In the context of counting onto functions, this principle is used to subtract the functions that miss one or more elements of the codomain, thereby ensuring that only surjective functions are counted.

Combinatorial Counting of Functions

Counting functions between finite sets generally starts with the total number of possible mappings from the domain to the codomain and then applies additional constraints for specific types of functions, such as onto functions. This basic approach involves understanding the structure of mappings and applying combinatorial formulas or principles like inclusion-exclusion to achieve the correct count.

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