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Questions and Answers
In the twelvefold way in combinatorics, what is the general problem that is considered?
In the twelvefold way in combinatorics, what is the general problem that is considered?
- Enumeration of equivalence classes of functions (correct)
- Counting permutations and combinations
- Enumeration of subsets
- Classification of finite sets
What does it mean when a function f is injective?
What does it mean when a function f is injective?
- Each b in X may occur multiple times in the image of f
- Each a in N may be sent by f to any b in X
- Each value for a in N must be distinct from every other (correct)
- There must be at least one a in N such that f(a) = b for each b in X
What is the condition for a function to be surjective?
What is the condition for a function to be surjective?
- Each a in N may be sent by f to any b in X
- For each b in X there must be at least one a in N such that f(a) = b (correct)
- Each b in X may occur multiple times in the image of f
- Each value for a in N must be distinct from every other
When is 'f is bijective' considered as an option?
When is 'f is bijective' considered as an option?
What does 'No condition' imply for the function f?
What does 'No condition' imply for the function f?
Which mathematician is credited with the idea of the classification known as the twelvefold way?
Which mathematician is credited with the idea of the classification known as the twelvefold way?
In how many ways can the three conditions on the functions and the four equivalence relations be paired?
In how many ways can the three conditions on the functions and the four equivalence relations be paired?
Which of the following is equivalent to counting n-permutations of X?
Which of the following is equivalent to counting n-permutations of X?
What does counting n-combinations of X correspond to?
What does counting n-combinations of X correspond to?
When n = x, counting permutations of the set X is equivalent to counting:
When n = x, counting permutations of the set X is equivalent to counting:
What is equivalent to counting partitions of the set N into x subsets?
What is equivalent to counting partitions of the set N into x subsets?
What does counting compositions of the number n into x parts correspond to?
What does counting compositions of the number n into x parts correspond to?
What is reflected by the property that any ball can go into only one box?
What is reflected by the property that any ball can go into only one box?
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