For each relation given below determine whether it is reflexive, irreflexive or neither; symmetric, asymmetric, antisymmetric, or
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For each relation given below determine whether it is reflexive, irreflexive or neither; symmetric, asymmetric, antisymmetric, or none of the above; transitive or not. Rom this determine whether it is a partial order, strict partial order, equivalence relation or none of the above.
a. The relationship of the natural numbers (a, b) ∈ R if and only if a = b + 1
b. The divides relation on N (a, b) ∈ R if and only if a|b
c. The divides relation on Z.
d. Given a function f (x) from the real numbers to the real numbers, let (a, b) ∈ R if and only if f (a) = f (b).
Related Book For
College Algebra Graphs and Models
ISBN: 978-0321845405
5th edition
Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna
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