- Problem 5 20 Marks Let Rc S X S Be Any Binary Relation On A Set S Consider The Sequence Of Relations Ro R R 1 (43.49 KiB) Viewed 49 times
- Problem 5 20 Marks Let Rc S X S Be Any Binary Relation On A Set S Consider The Sequence Of Relations Ro R R 2 (49.25 KiB) Viewed 49 times
Problem 5 (20 marks) Let RC S x S be any binary relation on a set S. Consider the sequence of relations Rº, R¹, R², ..., as follows: defined R⁰ = I= {(x,x): x € S}, and R"+1 := R" U (R; R") for n ≥ 0
(d) If |S| = k, explain why Rk² = R²+1 (e) If |S|=k, show that Rk² is transitive. (2 marks) (2 marks) (f)* If |S| = k show that R² is the minimum (with respect to C) of all reflexive and transitive relations that contain R. (4 marks)