16.1. Relations

Try these first

1. 1.

   Define what a relation is in your own words.

   Hint

   Think about pairs coming from two different sets.

2. 2.

   Give an example of a binary relation.

   Hint

   Consider relationships in terms of pairs from two sets.

3. 3.

   What is a relation?

   Hint

   Think about pairs from two different sets.

4. 4.

   True or False: A reflexive relation must have at least one element in a set.

   • True
   • False

   Hint

   Consider the case when no elements are present.

5. 5.

   Given sets A = {x, y, z} and B = {1, 2}, create three different binary relations and discuss their properties.

   Hint

   Think about how each relation captures different aspects of interaction.

6. 6.

   If set A = {a, b} and set B = {1, 2} are given, can you represent a reflexive relation in a matrix that also shows one additional non-reflexive pair?

   Hint

   Be creative with your definitions, but keep reflexivity in mind!