Read the given information carefully and answer the questions below:

1%2 means 2 is neither smaller nor greater than 1
1&2 means 2 is neither greater nor equal to 1
1*2 means 2 is neither smaller nor equal to 1
1$2 means 2 is not greater than 1
1α2 means 2 is not smaller than 1

Statements: W*RαP; L%M$R&S; W$H%Q
Conclusions: I. M $H II. L*Q III. P&S

The correct option is Only III is true.

Step 1: Decoding the symbols

Let us translate each given symbol based on the relationship between element 1 and element 2:
• 1 % 2 means "2 is neither smaller nor greater than 1", which means 2 = 1 (or 1 = 2).
• 1 & 2 means "2 is neither greater nor equal to 1", which means 2 < 1, so 1 > 2.
• 1 * 2 means "2 is neither smaller nor equal to 1", which means 2 > 1, so 1 < 2.
• 1 $ 2 means "2 is not greater than 1", which means 2 ≤ 1, so 1 ≥ 2.
• 1 α 2 means "2 is not smaller than 1", which means 2 ≥ 1, so 1 ≤ 2.

Summary of symbols (1 to 2):
• % means =
• & means >
• * means <
• $ means ≥
• α means ≤

Step 2: Decoding the given statements

Statement 1: W * R α P
• W * R ⇒ W < R
• R α P ⇒ R ≤ P
Combining: W < R ≤ P

Statement 2: L % M $ R & S
• L % M ⇒ L = M
• M $ R ⇒ M ≥ R
• R & S ⇒ R > S
Combining: L = M ≥ R > S

Statement 3: W $ H % Q
• W $ H ⇒ W ≥ H
• H % Q ⇒ H = Q
Combining: W ≥ H = Q

Combined Relationship Chain:
Q = H ≤ W < R ≤ M = L
and R > S, R ≤ P

Step 3: Evaluating the Conclusions

Conclusion I: M $ H
Decoding M $ H: M ≥ H.
From the combined chain: M ≥ R > W ≥ H, which implies M > H.
Since M is strictly greater than H, M ≥ H ($) is not necessarily true (M > H is the exact relation). Thus, Conclusion I is false.

Conclusion II: L * Q
Decoding L * Q: L < Q.
From the combined chain: L = M ≥ R > W ≥ Q, which implies L > Q.
Thus, L * Q (L < Q) is false.

Conclusion III: P & S
Decoding P & S: P > S.
From the given relationships, P ≥ R and R > S.
Combining these gives P > S.
Thus, Conclusion III is true.

Therefore, only Conclusion III is true.