16.2.4. Representation of Binary Relations

Try these first

1. 1.

   Define what a binary relation is.

   Hint

   Think about how sets interact with each other.

2. 2.

   What does a matrix representation of a binary relation do?

   Hint

   Consider what 1 and 0 might represent in the context of relations.

3. 3.

   What is a binary relation?

   Hint

   Think about how we define relationships in mathematics.

4. 4.

   True or False: Every binary relation has at least one pair.

   • True
   • False

   Hint

   Consider the definition of how relations can be formed.

5. 5.

   Given sets A = {1, 2, 3} and B = {A, B}, list all possible binary relations between these sets and determine the number of distinct relations.

   Hint

   Think about how many combinations there can be from A x B.

6. 6.

   Construct a directed graph for the relation R defined on set A = {1, 2} with entries {(1, 1), (1, 2), (2, 2)}. Identify the type of relation.

   Hint

   Check if all elements in set A connect back to themselves.