For each relation below, explain why the relation does or does not satisfy each of the properties
Question:
For each relation below, explain why the relation does or does not satisfy each of the properties reflexive, symmetric, antisymmetric, and transitive.
(a) "isBrotherOf" on the set of people.
(b) "isFatherOf" on the set of people.
(c) The relation R = {(x,y) | x^2 + y^2 = 1} for real numbers x and y.
(d) The relation R = {(x,y) | x^2 = y^3} for real numbers x and y.
(e) The relation R = {(x,y) | x mod y = 0} for x, y ∈ {1, 2, 3, 4}.
(f) The empty relation ∅ (i.e., the relation with no ordered pairs for which it is true) on the set of integers.
(g) The empty relation ∅ (i.e., the relation with no ordered pairs for which it is true) on the empty set.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Practical Introduction To Data Structures And Algorithm Analysis Java Edition
ISBN: 9780136609117
1st Edition
Authors: Clifford A. Shaffer
Question Posted: