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* = R i .