Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if
a) x + y = 0
b) x= ±y.
c) x-y is a rational number.
d) = 2y.
e) xy ≥ 0.
f) xy = 0.
g) x=l.
h) r=1 or y = 1
Determine whether the relation R on the set of all real numbers is reflexive, symmetric,...
For each of the following relations on the set of all real numbers, decide whether or not the relation is reflexive, symmetric, antisymmetric, and/or transitive. Give a brief explanation of why the given relation either has or does not have each of the properties. (x, y) elementof R if and only if: a. x + y = 0 b. x - y is a rational number (a rational number is a number that can be expressed in the form a/b...
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(1) For each of the following relations on R, is the relation reflexive? Is it symmetric? Is it transitive? (a)r1={(x, y)∈ R × R | xy= 0} (b) r2={(x, y)∈R×R|x2+y2= 1} (c)r3={(x, y)∈R×R||x−y|<5}
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