18.4. Composition of Relations

Try these first

1. 1.

   What is the intersection of R1 = {(1, 2), (2, 3)} and R2 = {(2, 3), (3, 4)}?

   Hint

   Find the common pairs present in both relations.

2. 2.

   If R3 = {(a, b), (b, c)} and R4 = {(b, c), (c, d)}, what is R3 ∪ R4?

   Hint

   Combine all pairs from both sets.

3. 3.

   The union of two relations R and S includes pairs where:

   • R pairs only
   • S pairs only
   • Pairs in either R or S

   Hint

   Remember what union means in set theory.

4. 4.

   True or False: The intersection of R1 and R2 can be empty if both relations are completely disjoint.

   • True
   • False

   Hint

   Think about what intersection means.

5. 5.

   Given R = {(1, 2), (2, 3), (3, 4)} and S = {(2, 3), (3, 5)}, compute R o S and explore the meaning behind it.

   Hint

   Think about how pairs connect to meet through mutual relationships.

6. 6.

   Construct and explain the symmetric closure of R = {(1, 2), (2, 3)}.

   Hint

   Consider what happens to asymmetric relations!