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: U$LαK%T; W&P; D*J; W%R$L; M*TαJ
Conclusions: I. M*W II. D&K III. J$P

Correct Answer: None is true

To solve this coded inequality question, let us first decode the given symbols according to the instructions provided:

1. 1%2 means 2 is neither smaller nor greater than 1 ⇒ 2 = 1 (or 1 = 2).

2. 1&2 means 2 is neither greater nor equal to 1 ⇒ 2 < 1 (which means 1 > 2).

3. 1*2 means 2 is neither smaller nor equal to 1 ⇒ 2 > 1 (which means 1 < 2).

4. 1$2 means 2 is not greater than 1 ⇒ 2 ≤ 1 (which means 1 ≥ 2).

5. 1α2 means 2 is not smaller than 1 ⇒ 2 ≥ 1 (which means 1 ≤ 2).

Now, let us rewrite the given relations for two elements A and B where A [symbol] B:

• A % B ⇒ A = B
• A & B ⇒ A > B
• A * B ⇒ A < B
• A $ B ⇒ A ≥ B
• A α B ⇒ A ≤ B

Given Statements:

• U $ L α K % T ⇒ U ≥ L, L ≤ K, K = T ⇒ U ≥ L ≤ K = T
• W & P ⇒ W > P
• D * J ⇒ D < J
• W % R $ L ⇒ W = R ≥ L
• M * T α J ⇒ M < T ≤ J

Combining the relevant statements to check each conclusion:

Conclusion I: M * W

M * W means M < W.

Combining the path between M and W:

M < T = K ≥ L ≤ R = W

Since the symbols between T and R change direction (K ≥ L ≤ R), there is no definite relationship between M and W. Thus, Conclusion I does not follow.

Conclusion II: D & K

D & K means D > K.

Combining the path between D and K:

D < J ≥ T = K

Since the symbols between D and K change direction (D < J ≥ T), there is no definite relationship between D and K. Thus, Conclusion II does not follow.

Conclusion III: J $ P

J $ P means J ≥ P.

Connecting J and P:

J ≥ T = K ≥ L ≤ R = W > P

Here also, opposite sign directions exist between J and P (K ≥ L ≤ R). Hence, no definite relationship can be established between J and P. Thus, Conclusion III does not follow.

Therefore, none of the conclusions I, II, or III are true.