18. Operations on Relations

Try these first

1. 1.

   Define the union of two relations.

   Hint

   Think about what happens to overlapping pairs.

2. 2.

   What is the intersection of two relations?

   Hint

   What do they have in common?

3. 3.

   What does the union of two relations consist of?

   • Only pairs from one relation
   • All pairs from both relations
   • Only unique pairs

   Hint

   Think of taking both sets together.

4. 4.

   True or False: The composition of two relations is always commutative.

   • True
   • False

   Hint

   Consider examples of R o S and S o R.

5. 5.

   Given relations R = {(1,2), (2,3)} and S = {(3,4), (2,4)}, find the composition R o S, then calculate the powers R^2 and the closure for reflexivity.

   Hint

   Build step by step: Composition first, then powers.

6. 6.

   Examine the relation T = {(1, 2), (2, 3)} and its symmetric closure. After defining the symmetric closure, determine if T is itself symmetric.

   Hint

   Draw T and visualize; determine pairs that must be added for symmetry.