Given the following symbols representing family relationships:

- $P \; @ \; Q$ means $P$ is the son of $Q$
- $P \; \wedge \; Q$ means $P$ is the father of $Q$
- $P \; \div \; Q$ means $P$ is the brother of $Q$
- $P \; + \; Q$ means $P$ is the daughter of $Q$
- $P \; - \; Q$ means $P$ is the mother of $Q$
- $P \; = \; Q$ means $P$ is the sister of $Q$
- $P \; \% \; Q$ means $P$ is the husband of $Q$

Which of the following expressions correctly represents that **E is the maternal grandmother of A**?

Question

Given the following symbols representing family relationships:

- $P \; @ \; Q$ means $P$ is the son of $Q$
- $P \; \wedge \; Q$ means $P$ is the father of $Q$
- $P \; \div \; Q$ means $P$ is the brother of $Q$
- $P \; + \; Q$ means $P$ is the daughter of $Q$
- $P \; - \; Q$ means $P$ is the mother of $Q$
- $P \; = \; Q$ means $P$ is the sister of $Q$
- $P \; \% \; Q$ means $P$ is the husband of $Q$

Which of the following expressions correctly represents that **E is the maternal grandmother of A**?

Accepted Answer

**Solution:**

1. We need to verify which expression correctly states that **E is the maternal grandmother of A**.

2. Recall the symbols:
   - $P - Q$: $P$ is the mother of $Q$
   - $P + Q$: $P$ is the daughter of $Q$
   - $P = Q$: $P$ is the sister of $Q$
   - $P \div Q$: $P$ is the brother of $Q$
   - $P \% Q$: $P$ is the husband of $Q$

3. The maternal grandmother of $A$ is the mother of $A$'s mother.

4. Let's analyze option (e): $A + D = C \div B \% E$

- $A + D$: $A$ is the daughter of $D$ → $D$ is the parent of $A$ (gender not specified yet).
   - $D = C$: $D$ is the sister of $C$ → $D$ and $C$ are siblings.
   - $C \div B$: $C$ is the brother of $B$ → $C$ and $B$ are siblings.
   - $B \% E$: $B$ is the husband of $E$ → $E$ is wife of $B$.

5. From above, $D$ is sister of $C$, and $C$ is brother of $B$, so $B$, $C$, and $D$ are siblings.

6. Since $B$ is husband of $E$, $E$ is the wife of $B$.

7. $D$ is mother of $A$ (since $A + D$ means $A$ is daughter of $D$), so $D$ is female.

8. $D$ and $B$ are siblings, so $B$ is $D$'s brother.

9. $E$ is wife of $B$, so $E$ is mother of $D$'s children if any, but here $E$ is mother of $D$'s sibling's children.

10. Since $D$ is mother of $A$, and $E$ is mother of $B$, who is brother of $D$, $E$ is the mother of $D$ (because $B$ and $D$ are siblings, and $E$ is wife of $B$), so $E$ is the mother of $D$'s sibling, which means $E$ is the mother of $D$ and $C$ and $B$.

11. Therefore, $E$ is the mother of $D$, who is mother of $A$, so $E$ is maternal grandmother of $A$.

**Answer:** Option (e) $A + D = C \div B \% E$ correctly represents that $E$ is the maternal grandmother of $A$.

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