18.3. Difference of Relations

Try these first

1. 1.

   What is the result of the union of R1 = {(1, 2)} and R2 = {(2, 3)}?

   Hint

   Think about combining all pairs.

2. 2.

   If R1 = {(1, 2)} and R2 = {(1, 2)} then what is R1 ∩ R2?

   Hint

   Look for pairs that are in both sets.

3. 3.

   Which operation will yield all pairs (x, y) where x is not equal to y?

   • Union
   • Intersection
   • Difference

   Hint

   Remember what happens when you collect all unique pairs.

4. 4.

   True or False: The intersection of R1 and R2 can never be empty.

   • True
   • False

   Hint

   Consider examples where sets do not share elements.

5. 5.

   Given relations R1 = {(1, 2), (3, 4)} and R2 = {(2, 3), (4, 5)}, compose the two relations and find R1 o R2.

   Hint

   Trace the paths to find the pairs that link through common elements.

6. 6.

   Construct the reflexive closure for the relation R = {(1, 2), (2, 3)} on set A = {1, 2, 3}.

   Hint

   Ensure every element in A links to itself.