Two hats are picked at random, what is the probability

Statement: A > U ≥ L; A ≤ T = K; J > U

Conclusion: I. K > L           II. J > T

Statements:

A ≥ L = B; C ≤ L < O; Q ≥ C < R

Conclusions:

I. A > C

II. C = A

Statements: F < G ≤ H; D < I; J ≥ G; F < A < D

Conclusions:

I. I > F

II. J > A

III. D > G

Statements:

R ≤ S = T; P < Q = R; S < U ≤ V; W ≥ V

Conclusions:

I).  P < U

II).  W > R

Statement: A > B = E < F > H; I ≤ D < C; H > G > C

Conclusions:

I. F > I

II. I < G

III. B < G

Statements: P % Q, P $ R, Q # S, R @ T

Conclusions:

I. R $ Q                     

Statement:X=Y ≥ Z > Q; Y < V ; W < Q

Conclusions:

I. V > W

II. Q > V

Statements: M = N; A < C < E; N > A

Conclusions:

I. E > N

II. M > C

Statements: L > S, O > Q, S = P, T ≥ P, O = T

Conclusion:

I. L ≥ Q

II. Q > L

Statements:        X @ Y % M % N; M $ P $ Z