17.5. Transitive Relations

Try these first

1. 1.

   Define a transitive relation in your own words.

   Hint

   Think about how relationships connect.

2. 2.

   Give an example of a transitive relation.

   Hint

   Consider family relations.

3. 3.

   What characterizes a transitive relation?

   • If aRb and bRc then aRc
   • If aRb then bRc
   • a is equal to b

   Hint

   Remember the relationship structure!

4. 4.

   True or False: All transitive relations are symmetric.

   • True
   • False

   Hint

   Consider the definitions of both properties.

5. 5.

   Consider a relation defined over a set A = {1, 2, 3}. Given pairs are {(1, 2), (2, 3), (1, 3)}. Is this relation transitive? Justify your answer.

   Hint

   Check all the necessary conditions for transitivity.

6. 6.

   Construct a non-transitive relation over the set {1, 2, 3} and prove it is not transitive.

   Hint

   Focus on withdraw pair conditions.