Determine whether the relation R on the set of all real numbers is reflexive, symmetric,...

Question:

Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where {eq}\displaystyle (x,y)\in R {/eq} if and only if

{eq}a.\ x+y=0\\[2ex] b.\ x=\pm y\\[2ex] c.\ x-y \text{ is a rational number.}\\[2ex] d.\ x=2y\\[2ex] e.\ xy\geq 0\\[2ex] f.\ xy=0\\[2ex] g.\ x=1\\[2ex] h.\ x=1\text{ or } y=1 {/eq}

Discrete Mathematics:

Discrete Mathematics is a combination of Maths and algebra. The mathematics used in particular combinatorics and graph theory.

Answer and Explanation:

a) R={ (x,y)| x+y=0} x+y=0 or y+x=0 both are same

The relation is SYMMETRIC.

A relation is Symmetric When (a,b)? R then (b, a)? R

b)...

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from PSAT Prep: Tutoring Solution

Chapter 10 / Lesson 13
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