Practice Question 8: Functions From Set X To Set Y (2.4)

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6 sample questions

Question 1.
What is the total number of functions from a set with 2 elements to a set with 3 elements?
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Use the formula n^m.
Question 2.
Define an injective function.
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Think about how elements can pair uniquely.
3Question 3.
What is the formula to find the total number of functions from set X to set Y?
- m^n
- n^m
- m+n
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Think about how many options each element has.
4Question 4.
True or False: An injective function can map distinct elements of X to the same element of Y.
- True
- False
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Consider the nature of injective relationships.
Question 5.
Prove that if there are more elements in set X than set Y (m > n), then the number of injective functions is zero.
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Consider the definition of injective functions.
Question 6.
Calculate the Stirling number S(5, 3) and explain the method of your calculation.
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Think of splitting the set into distinct groups.

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