21.5.3. Part C: Symmetric and Anti-Symmetric Relations

Try these first

1. 1.

   Define a symmetric relation and provide one example.

   Hint

   Think about relationships where both parties have mutual recognition.

2. 2.

   What characterizes an anti-symmetric relation?

   Hint

   Consider scenarios where equality plays a role.

3. 3.

   True or False: A symmetric relation must have both (a,b) and (b,a) present if one exists.

   • True
   • False

   Hint

   Check how the elements must relate to each other.

4. 4.

   The number of symmetric relations on a set of size n is given by which formula?

   Hint

   Remember the half counts in pairing.

5. 5.

   Given a set of size 5, calculate the total number of symmetric relations. Show the step-by-step process.

   Hint

   Recall the formula involves n choose pairs.

6. 6.

   Construct a set of elements and create both a symmetric and an anti-symmetric relation. Explain the choices.

   Hint

   Think about the directionality involved.