Given the following coding symbols and their meanings:

- $a \% b$ means $b$ is neither smaller nor greater than $a$
- $a \& b$ means $b$ is neither greater nor equal to $a$
- $a * b$ means $b$ is neither smaller nor equal to $a$
- $a \$ b$ means $b$ is not greater than $a$
- $a \alpha b$ means $b$ is not smaller than $a$

Analyze the following statements and determine which conclusions are true:

Statements:

- $W * R \alpha P$
- $L \% M \$ R \& S$
- $W \$ H \% Q$

Conclusions:

I. $M \$ H$

II. $L * Q$

III. $P \& S$

Question

Given the following coding symbols and their meanings:

- $a \% b$ means $b$ is neither smaller nor greater than $a$
- $a \& b$ means $b$ is neither greater nor equal to $a$
- $a * b$ means $b$ is neither smaller nor equal to $a$
- $a \$ b$ means $b$ is not greater than $a$
- $a \alpha b$ means $b$ is not smaller than $a$

Analyze the following statements and determine which conclusions are true:

Statements:

- $W * R \alpha P$
- $L \% M \$ R \& S$
- $W \$ H \% Q$

Conclusions:

I. $M \$ H$

II. $L * Q$

III. $P \& S$

Accepted Answer

**Solution:** Let's analyze the given statements and conclusions step-by-step using the provided symbol meanings. **Given symbol meanings:** - $a \% b$: $b$ is neither smaller nor greater than $a$ (means $a = b$) - $a \& b$: $b$ is neither greater nor equal to $a$ (means $b < a$) - $a * b$: $b$ is neither smaller nor equal to $a$ (means $b > a$) - $a \$ b$: $b$ is not greater than $a$ (means $b \leq a$) - $a \alpha b$: $b$ is not smaller than $a$ (means $b \geq a$) --- **Statements:** 1. $W * R \alpha P$ - $W * R$ means $R > W$ - $R \alpha P$ means $P \geq R$ - So, $R > W$ and $P \geq R$ imply $P \geq R > W$ 2. $L \% M \$ R \& S$ - $L \% M$ means $M = L$ - $M \$ R means $R \leq M$ - $R \& S$ means $S < R$ - Combining: $M = L$, $R \leq M$, and $S < R$ 3. $W \$ H \% Q$ - $W \$ H means $H \leq W$ - $H \% Q$ means $Q = H$ - So, $Q = H \leq W$ --- **Conclusions:** I. $M \$ H$ means $H \leq M$ - From statements, $M = L$ and $H \leq W$ but no direct relation between $M$ and $H$ is given. - Since $L$ and $W$ are unrelated in the statements, we cannot confirm $H \leq M$. - So, conclusion I is **false**. II. $L * Q$ means $Q > L$ - From statements, $M = L$, $Q = H \leq W$, and $R > W$. - No direct comparison between $Q$ and $L$ is given. - So, conclusion II cannot be confirmed and is **false**. III. $P \& S$ means $S < P$ - From statements, $P \geq R > W$, and $S < R$. - Since $P \geq R$ and $S < R$, it follows that $S < P$. - So, conclusion III is **true**. --- **Answer:** Only conclusion III is true.

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