For the following relations on the set of points on the plane, determine if it s

Question

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

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

Explanation / Answer

......................................................................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

(u1, u2) ? (w1, w2) ? u1 = w1

Y N Y N

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

Y Y Y Y

line segment joining the two points have a slope > 16

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

N

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