NOTE: THIS IS CHAPTER 3 - RELATIONS- IN "DISCRETE MATHEMATICS" (AKA DISCRETE STRUCTURE) COURSE FOR COMPUTER SCIENCE**

EXERCISE 3.2.1: Identifying properties of relations. For each relation, indicate whether the relation is: reflexive, anti-reflexive, or neither symmetric, anti-symmetric, or neither transitive or not transitive . (a) The domain of the relation L is the set of all real numbers. For x, y RXLy if x (b) The domain of the relation E is the set of all real numbers. For x, y ER, xEy if x s y ( The domain of relation P is the set of all positive integers. Forxy cZ".xPy if there is a positive integer n such that (c) n The domain for the relation D is the set of all integers. For any two integers, x and y, xDy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.) (d) (e) The domain for the relation A is the set of all real numbers. xAy if Ix-yl s 2 The domain for relation R is the set of all real numbers. xRy if x-y is rational. A real number r is rational if there are two integers a and b, such that b rational. (f) 0 and r = a/b. You can use the fact that the sum of two rational numbers is also g) The domain for the relation is ZxZ. (a, b) is related to (c, d) if a s c and bs d. h) The domain for the relation is ZxZ. (a, b) is related to (c, d) if a s c or bs d (inclusive or) (i) The domain for relation T is the set of real numbers. XTy if x + y = 0. O) The domain for relation Z is the set of real numbers. xZy if y 2x. The domain for relation Tis a group of people. xTy if person y is taller than person x. There are at least two people in the group who are not the same height