Which heuristic function property ensures A* algorithm

Statements: Q > W > X; J > W; Z < X < P

Conclusions:

I. P > Z

II. J > Q

III. W < P

Statements:

T % W % B $ I @ L

Conclusions:

I. B * T

II. L © B

III. L * T

Statements: S ≥ T = U > V, W < T ≤ P > X

Conclusion:

I. V ≥ X

II. W < S

Statements:   A % I, I  *  Q, Q % R, R $ M

Conclusions :

I.  M # I

II. M # Q

III. I # R

IV. Q % A

Statement: V > R; C > U > Q; C < R

Conclusion:

I.V > Q

II. V > U

Statements : C © S * R, U % R $ Z 

Conclusions : 

I. Z $ C 

II. U % S 

III. U © C

Statements: F > V > W ≥ L > G; F ≤ O = M < I

Conclusions: I. M > L     II. V < I

Statements: U < P = I ≤ V < T ≤ R = W > H = Z > O

Conclusions:

I. U < W

II. R > O