16.2.2. Binary Relations

Try these first

1. 1.

   Define a binary relation using sets A = {1, 2, 3} and B = {a, b}.

   Hint

   Remember to pair elements from A to those in B.

2. 2.

   What does reflexivity mean in terms of relations?

   Hint

   Consider how elements interact with themselves.

3. 3.

   What is a binary relation?

   • A single ordered pair
   • A subset of the Cartesian product of two sets
   • A property of a single set

   Hint

   Think about how relations link elements from two different sets.

4. 4.

   True or False: A reflexive relation can contain elements that do not relate to themselves.

   • True
   • False

   Hint

   Revisit the definition of reflexivity.

5. 5.

   Prove that if R is a reflexive relation on a set A, then R must include (a, a) for every a in A.

   Hint

   Refer back to the definition of reflexivity.

6. 6.

   Given sets A = {1, 2, 3} and B = {x, y}, list all possible binary relations and count them.

   Hint

   Consider how many ways you can select pairs from the Cartesian product.