Mod 2

Question 1

Weak preference relation

Answer 1

x is as least as good as y
or y is no better than x

Question 2

Strict preference relation

Answer 2

x is preferred to y, must satisfy the weak preference.

Question 3

Indifferent

Answer 3

x is equal to y

Question 4

BR1

Answer 4

Reflexivity

Question 5

Reflexivity

Answer 5

xRx, x is related to its self

eg. weak preference realtion should satisfy this, “equality”

Question 6

BR2

Answer 6

Irreflexive

Question 7

Irreflexive

Answer 7

For all of x in X no xRx. opposite of reflexive.

e.g strictly greater than.

Question 8

BR3

Answer 8

Completeness

Question 9

Completeness

Answer 9

For all X & Y in X either xRy or yRx (or both)

if you have two bundles of goods at least the first bundle is as good as the second or vice versa.

Weak preference is complete

Question 10

BR4

Answer 10

Transitivity

Question 11

Transitivity

Answer 11

For all x, y & z in X if xRy & yRz the xRz

e.g if x is as least as great as y and y is as least as great as z then x is as least as great as z

Question 12

BR5

Answer 12

Negative Transitivity

Question 13

Negative Transitivity

Answer 13

For all x,y, z in X if xRy then either xRz or zRy or both

Question 14

BR6

Answer 14

Symmetry

Question 15

Symmetry

Answer 15

For all x & y in X if xRy then yRx

indifferent, not worried about direction

Question 16

BR7

Answer 16

Antisymmetric

Question 17

Antisymmetric

Answer 17

For all x & y in X if XRy & yRx then x=y

Question 18

BR8

Answer 18

Asymmetry

Question 19

Asymmetry

Answer 19

For all x & y in X if xRy then not yRx

implied by irreflexive

Question 20

What do BR3 and BR4 define

Answer 20

weak preferences

Question 21

What do BR2 and BR5 define

Answer 21

Strict preferences

Question 22

What do BR1, BR4 and BR6 satisfy

Answer 22

indifferent relations

Question 23

Weak order

Answer 23

transitive and complete

Question 24

strict partial order

Answer 24

transitive and asymmetric

Question 25

equivalence

Answer 25

reflexive, symmetric, transitive

Question 26

if weak preference not complete then

Answer 26

incomparable

Question 27

If weak preference is transitive and complete then

Answer 27

strict preference is transitive and irreflexive indifference relation is reflexive, symmetric, transitive

Question 28

The strict preference relation is rational if it is

Answer 28

both asymmetric and negatively transitive

Question 29

The strict preference relation is both asymmetric and negatively transitive (rational) then it is

Answer 29

also irreflexive and transitive

Question 30

that completeness implies reflexivity,

Answer 30

To show that it is reflexive we must show that for all x in X we have xRx. But since the relation is complete we have, for any y and z in X either yRz or zRy. In particular if we let y = x and z = x then we have either xRx or xRx, that is, xRx, as required.