Practice - Question 10: Relations and Functions
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Practice Questions
Test your understanding with targeted questions
What does reflexivity mean in the context of equivalence relations?
💡 Hint: Think of what happens when you compare an element to itself.
Define a surjective function in simple terms.
💡 Hint: Consider how each element in the output set is associated.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What characterizes a bijective function?
💡 Hint: Think about the definitions of injective and surjective.
True or False: A surjective function guarantees that all outputs are unique.
💡 Hint: Consider mappings where elements can overlap.
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Challenge Problems
Push your limits with advanced challenges
Determine and justify whether the relation defined on the set {1, 2, 3} with pairs {(1, 2), (2, 1), (2, 3)} is an equivalence relation.
💡 Hint: Examine each of the equivalence relation properties separately.
Calculate the number of surjective functions from a set with 3 distinct elements to a set with 2 distinct elements, employing the Stirling function.
💡 Hint: Break it down using partitions and consider permutations!
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