Preference

Question 1

What is the reflexivity property of a binary relation?

Answer 1

xRx

Question 2

What is the Irreflexivity property of a binary relation?

Answer 2

¬(xRx)

Question 3

What is the Symetry property of a binary relation?

Answer 3

xRy ⇒ yRx

Question 4

What is the Asymetry property of a binary relation?

Answer 4

xRy ⇒ ¬ (yRx)

Question 5

What is the Antisymetry property of a binary relation?

Answer 5

xRyRx ⇒ x = y

Question 6

What is the Completeness property of a binary relation?

Answer 6

xRy ∨ yRx

Question 7

What is the Transitivity property of a binary relation?

Answer 7

xRyRz => xRz

Question 8

What is the Negative Transitivity property of a binary relation?

Answer 8

¬(xRy) ∧ ¬(yRx) => ¬(xRz)

Question 9

What is an equivalent relation?

Answer 9

Satisifes Symmetry and Transitivity

Question 10

What is a Partial order Relation?

Answer 10

Satisfies Reflexivity, Antisymetry and Transitivity

Question 11

What is a Strict order relation?

Answer 11

Satisifies Irreflexivity, Antysymetry, Transitivity

Question 12

What is a pre order relation?

Answer 12

Satisifies reflexivity and Transitivity

Question 13

What is a Weak order relation?

Answer 13

Satisifies Completeness and Transitivity

Question 14

What is a rational preference?

Answer 14

It is a weak order relation => complet and transitive

Question 15

If ≽ is rational, then…

Answer 15

1) ∼ is an equivalent relation
2) ≽ = non ≺
3) ≻ is asymetric, transitive ad negatively transitive
4) x ≻ y ≽ z => x ≻ z

Question 16

What is a ≽-best element?

Answer 16

x is a ≽-best element if, for every y in X, x ≽y

Question 17

What is a ≽-maximum element?

Answer 17

x is a ≽-maximum element if for every y in X, y ≽ x implies x ≽ y

Question 18

If ≽ is rational then (≽-best)

Answer 18

1) x is a ≽-best element iff x is ≽-maximum element

2) If X is finite, then there exists a ≽-best element