In the following questions, the symbols $, %, @, © and  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  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., $P < Q$).
- $P 	o Q$ means $P$ is not greater than $Q$ (i.e., $P \leq Q$).
- $P \@ Q$ means $P$ is not smaller than $Q$ (i.e., $P \geq Q$).

Which of the following symbols should be placed in the blank spaces respectively (from left to right) to complete the expression such that the statements $H \© J \$ G$ and $E \@ F$ are true?

$$F \% G * E \_ J \$ I \% H$$

Options:

Accepted Answer

**Solution:** 1. Given the meanings of the symbols: - $P \% Q$: $P = Q$ - $P \$ Q$: $P > Q$ - $P \© Q$: $P < Q$ - $P o Q$: $P \leq Q$ - $P \@ Q$: $P \geq Q$ 2. The expression to complete is: $$F \% G * E \_ J \$ I \% H$$ 3. The conditions to satisfy are: - $H \© J \$ G$ is true, meaning $H < J > G$ - $E \@ F$ is true, meaning $E \geq F$ 4. From the first part, $H < J$ means the symbol between $H$ and $J$ must be $©$ (less than). 5. From the second part, $E \geq F$ means the symbol between $E$ and $F$ must be $@$. 6. Also, $F \% G$ means $F = G$, so the symbol between $F$ and $G$ is $%$. 7. The symbol between $J$ and $I$ is $\$$, meaning $J > I$. 8. Therefore, the symbols in order are: - Between $F$ and $G$: $%$ - Between $G$ and $E$: $*$ (unknown) - Between $E$ and $J$: $\_$ (unknown) - Between $J$ and $I$: $\$$ - Between $I$ and $H$: $%$ 9. To satisfy $E \geq F$, and given $F = G$, $E$ must be greater than or equal to $F$ and $G$, so the symbol between $G$ and $E$ should be $\$$ (greater than). 10. To satisfy $H < J$, the symbol between $E$ and $J$ should be $©$ (less than). 11. Hence, the symbols are: - $* = \$$ - $\_ = ©$ - $\$ = @$ **Answer:** Option 1: $* = \$, \_ = ©, \$ = @$

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