17.2. Symmetric Relations

Try these first

1. 1.

   Define a symmetric relation in your own words.

   Hint

   Think about bilateral relationships.

2. 2.

   Is the relation {(1, 1), (1, 2)} symmetric?

   Hint

   Check to see if the opposite pairs exist.

3. 3.

   What defines a symmetric relation?

   • If (a
   • b) implies (b
   • a)
   • If (a
   • b) implies (a
   • c)
   • If (a
   • a) is always present

   Hint

   Consider the pairs and their relationships.

4. 4.

   True or False: A reflexive relation is always symmetric.

   • True
   • False

   Hint

   Remember an example where reflexive does not mean symmetric.

5. 5.

   Construct a symmetric relation for a set A = {1, 2, 3} and explain its properties.

   Hint

   Ensure all necessary reciprocate pairs are included.

6. 6.

   Prove whether a relation defined as R = {(1, 2), (2, 3), (1, 3)} can be symmetric.

   Hint

   Check for reciprocal relationships.