21.1. Discrete Mathematics

Try these first

1. 1.

   Define a symmetric relation with an example.

   Hint

   Think of pairs and their reverse.

2. 2.

   What does it mean for A to be a subset of B?

   Hint

   Check if the elements of A are all included in B.

3. 3.

   What is a symmetric relation?

   • Only (a
   • b) exists
   • Both (a
   • b) and (b
   • a) exist
   • Neither exists

   Hint

   Recall how pairs behave in symmetric relations.

4. 4.

   True or False: Every reflexive relation is symmetric.

   • True
   • False

   Hint

   Think of reflexive definitions.

5. 5.

   Determine the number of reflexive relations on a set of size n.

   Hint

   Consider how diagonal elements limit your choices.

6. 6.

   If A is a set of n distinct elements, prove A can have at most 2^((n(n-1)/2) + n) distinct symmetric relations.

   Hint

   Think about each pairing and its count implications.