Let A be the set of all lines in the plane. Define a relation R on A as follows. For every l1 and l2 in A, l1 R l2 ⇔ l1 is parallel to l2. (Assume that a line is parallel to itself.) Which of the following is true for R? (Select all that apply.) R is reflexive. R is symmetric. R is transitive. R is neither reflexive, symmetric, nor transitive.

Let A be the set of all lines in the plane. Define a relation R on A as follows. For every l1 and l2 in A, l1 R l2 ⇔ l1 is parallel to l2. (Assume that a line is parallel to itself.) Which of the following is true for R? (Select all that apply.) R is reflexive. R is symmetric. R is transitive. R is neither reflexive, symmetric, nor transitive.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let A be the set of all lines in the plane. Define a relation R on A as follows.

For every

l₁

and

l₂

in A,

l₁ R l₂ ⇔ l₁

is parallel to

l₂.

(Assume that a line is parallel to itself.)

Which of the following is true for R? (Select all that apply.)

R is reflexive.

R is symmetric.

R is transitive.

R is neither reflexive, symmetric, nor transitive.

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