2.6. Question 10: Relations and Functions

Try these first

1. 1.

   What does reflexivity mean in the context of equivalence relations?

   Hint

   Think of what happens when you compare an element to itself.

2. 2.

   Define a surjective function in simple terms.

   Hint

   Consider how each element in the output set is associated.

3. 3.

   What characterizes a bijective function?

   • It is injective
   • It is surjective
   • Both injective and surjective

   Hint

   Think about the definitions of injective and surjective.

4. 4.

   True or False: A surjective function guarantees that all outputs are unique.

   • True
   • False

   Hint

   Consider mappings where elements can overlap.

5. 5.

   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.

6. 6.

   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!