Unit 20 Exercises

1. Let R be the parent-child relation on the set of people that is, R = { (a, b) | a is a parent of b }.  Let S be the sibling relation on the set of people that is, R = { (a, b) | a and b are siblings (brothers or sisters) }.  What are S oR and R oS  ?

2. Let R be a reflexive relation on a set A.  Show that R n is reflexive for all positive intergers n.

3. Let R be the relation on the set { 1, 2, 3, 4} containing the ordered pairs (1, 1), (1, 2), (2, 2), (2, 4), (3, 4), and (4, 1).  Find

a) the reflexive closure of R
b) symmetric closure of R  and
c) transitive closure of R.

4. Let R be the relation { (a, b) | a is a (integer) multiple of b } on the set of integers.  What is the symmetric closure of R  ?

5. Suppose that a binary relation R on a set A is reflexive.  Show that   R*   is reflexive,  where   R* = cup_n.gif 
(1023 bytes) R i .

 

Answers for these exercises