21.4.1. Part A: Symmetric Relations

Try these first

1. 1.

   Define a symmetric relation.

   Hint

   What must be true for pairs in symmetric relations?

2. 2.

   Give an example of a symmetric relation in everyday life.

   Hint

   Think of a reciprocal relationship.

3. 3.

   Which of the following defines a symmetric relation?

   • If (a
   • b) is in R
   • then (b
   • a) must also be in R.
   • If (a
   • b) is in R
   • then (b
   • c) must also be in R.
   • If (a
   • b) is not in R
   • then (b
   • a) must not be in R.

   Hint

   Think about the mutual involvement of pairs.

4. 4.

   True or False: A symmetric relation must contain both (a, b) and (b, a) for all elements.

   • True
   • False

   Hint

   Consider what happens when pairs are not included.

5. 5.

   Given a set of n elements, determine the total possible symmetric relations and explain the reasoning.

   Hint

   Recall how symmetry pairs require mutual inclusion.

6. 6.

   Consider the set A = {1, 2, 3}. Construct all symmetric relations possible and classify them.

   Hint

   List all pairs and check if they fulfill the symmetry condition.