Taken from Discrete Math and its Applications 7th edition, Ch 9.1 Problem #6 : D

Question

Taken from Discrete Math and its Applications 7th edition, Ch 9.1

Problem #6 :

Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive where (x,y) e R iff:

a) x+y = 0

c) x-y is a rational number

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For a) I'm pretty sure it's not reflexive (all elements have to map themselves), not transitive ( x=y, y=z, x=z). The issue I have is between symmetric and anti-symmetric. And I have the same issue with c).

Any help will be greatly appreciatied.

Explanation / Answer

a)symmetric

c)non-symmetric

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