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 â R, xLy if x < y.
b. The domain of the relation E is the set of all real numbers. For x, y â R, xEy if x ⤠y.
c. The domain of relation P is the set of all positive integers. For x, y â Z+, xPy if there is a positive integer n such that xn = y.
d. 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.)
e. The domain for the relation A is the set of all real numbers. xAy if |x - y| ⤠2.