21.4. Question 3

Try these first

1. 1.

   What is a symmetric relation?

   Hint

   Consider how pairs are related.

2. 2.

   Provide an example of an anti-symmetric relation.

   Hint

   Think about how elements relate when they are equal.

3. 3.

   Which of the following pairs must both be present for a symmetric relation?

   • (i
   • j)
   • (i
   • j)
   • (j
   • i)
   • (i
   • k)

   Hint

   Think about how the pairs relate to each other.

4. 4.

   True or False: All reflexive relations are also symmetric.

   • True
   • False

   Hint

   Consider the definitions of both properties.

5. 5.

   Given a set of 5 elements, calculate the number of different symmetric relations possible. Show your workings.

   Hint

   Focus on how each pair can be chosen.

6. 6.

   Explain why a relation that is both reflexive and asymmetric cannot exist. Provide a contradiction.

   Hint

   Consider the definitions and how they interact.