In the following questions, the symbols $, %, @, © and $\to$ are used with the following meanings: - $P \% Q$ means $P$ is neither greater than nor smaller than $Q$ (i.e., $P = Q$) - $P \$ Q$ means $P$ is neither smaller than nor equal to $Q$ (i.e., $P Q$) - $P \© Q$ means $P$ is neither greater than nor equal to $Q$ (i.e., $P

Question

In the following questions, the symbols $, %, @, © and $\to$ are used with the following meanings:

- $P \% Q$ means $P$ is neither greater than nor smaller than $Q$ (i.e., $P = Q$)
- $P \$ Q$ means $P$ is neither smaller than nor equal to $Q$ (i.e., $P > Q$)
- $P \© Q$ means $P$ is neither greater than nor equal to $Q$ (i.e., $P < Q$)
- $P \to Q$ means $P$ is not greater than $Q$ (i.e., $P \leq Q$)
- $P @ Q$ means $P$ is not smaller than $Q$ (i.e., $P \geq Q$)

**Question:**

In which of the following expressions are the statements $P @ Q$ and $M \© L$ **not definitely true**?

Accepted Answer

**Solution:**

1. First, understand the meaning of each symbol:
   - $P \% Q$ means $P = Q$
   - $P \$ Q$ means $P > Q$
   - $P \© Q$ means $P < Q$
   - $P \to Q$ means $P \leq Q$
   - $P @ Q$ means $P \geq Q$

2. We need to find the expression where $P @ Q$ (i.e., $P \geq Q$) and $M \© L$ (i.e., $M < L$) are **not definitely true**.

3. Analyze option (c): $P \© R @ Q \% M * N * L$
   - Here, $P \© R$ means $P < R$
   - $R @ Q$ means $R \geq Q$
   - $Q \% M$ means $Q = M$
   - $M * N * L$ involves symbols not defined in the question, but assuming $*$ is a placeholder or typo, the key relations are:

From $P < R \geq Q = M$, it implies:
   - $P < R$
   - $R \geq Q$
   - $Q = M$

Since $P < R$ and $R \geq Q$, it is possible that $P < Q$, so $P \geq Q$ (i.e., $P @ Q$) is **not definitely true**.

Also, $M = Q$ and no clear relation to $L$ is given, so $M < L$ ($M \© L$) is **not definitely true**.

4. In other options, the relations ensure $P \geq Q$ and $M < L$ hold definitely.

**Answer:** Option (c) is the only expression where $P @ Q$ and $M \© L$ are not definitely true.

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