For the following relations on the set of points on the plan

For the following relations on the set of points on the plane, determine if it satisfies each of the following conditions (please enter Y or N in each of the boxes):

Reflexive

Symmetric

Transitive

Equivalence Relation

(u₁, u₂) ? (w₁, w₂) ? u₁ = w₁

(x₁, y₁) ? (x₂, y₂) ? either (x₁, y₁)=(x₂, y₂) or the

line segment joining the two points have a slope > 16

(x₁, y₁) ? (x₂, y₂) ? the distance between the points is > 2

Solution

_{......................................................................REFLEXIVE SYMMETRIC TRANSITIVE EQUIVAL.}

(u₁, u₂) ? (w₁, w₂) ? u₁ = w₁

(x₁, y₁) ? (x₂, y₂) ? either (x₁, y₁)=(x₂, y₂) or the

line segment joining the two points have a slope > 16

(x₁, y₁) ? (x₂, y₂) ? the distance between the points is > 2

(x₁, y₁) ? (x₂, y₂) ? the distance between the points is > 2.....NOT REFLEXIVE......

SYMMETRIC .....NOT TRANSITIVE ...NOTEQUIVALENCE