2.4. Question 8: Functions from Set X to Set Y

Try these first

1. 1.

   What is the total number of functions from a set with 2 elements to a set with 3 elements?

   Hint

   Use the formula n^m.

2. 2.

   Define an injective function.

   Hint

   Think about how elements can pair uniquely.

3. 3.

   What is the formula to find the total number of functions from set X to set Y?

   • m^n
   • n^m
   • m+n

   Hint

   Think about how many options each element has.

4. 4.

   True or False: An injective function can map distinct elements of X to the same element of Y.

   • True
   • False

   Hint

   Consider the nature of injective relationships.

5. 5.

   Prove that if there are more elements in set X than set Y (m > n), then the number of injective functions is zero.

   Hint

   Consider the definition of injective functions.

6. 6.

   Calculate the Stirling number S(5, 3) and explain the method of your calculation.

   Hint

   Think of splitting the set into distinct groups.