Practice Onto Functions (16.5) - Valid Sequences Analysis - Discrete Mathematics

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6 sample questions

Question 1.
Define an onto function in your own words.
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Think about functions where every output has a corresponding input.
Question 2.
What condition must be met for a function to be considered onto?
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Consider what it means for something to be covered completely.
3Question 3.
What is an onto function?
- A function where not all outputs are covered
- A function where every output is covered by at least one input
- A function with no outputs
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Remember the definition of mapping in functions.
4Question 4.
True or False: A function can be onto if the domain has fewer elements than the codomain.
- True
- False
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Think about how functions work with outputs.
Question 5.
Given a set A with 6 elements and set B with 4 elements, determine how many onto functions can exist.
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Break it down using f(m, n) recursively.
Question 6.
Explain why the number of onto functions decreases as the size of the codomain grows beyond the domain.
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Think about coverage; if more elements exist in B than A, it can't map fully.

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