Given the following relationships:

- $X@Y$ means $X$ is son of $Y$
- $X#Y$ means $X$ is mother of $Y$
- $X$\$Y$ means $X$ is spouse of $Y$
- $X%Y$ means $X$ is daughter-in-law of $Y$
- $X*Y$ means $X$ is sister of $Y$
- $X&Y$ means $X$ is father of $Y$
- $X+Y$ means $X$ is grandmother of $Y$

Statements:

- $V$\$A + B$
- $E & T$
- $C # S * T$
- $B @ H % C$\$E$

If $Z * H$, then who among the following is sister-in-law of $Z$?

Question

Given the following relationships:

- $X@Y$ means $X$ is son of $Y$
- $X#Y$ means $X$ is mother of $Y$
- $X$\$Y$ means $X$ is spouse of $Y$
- $X%Y$ means $X$ is daughter-in-law of $Y$
- $X*Y$ means $X$ is sister of $Y$
- $X&Y$ means $X$ is father of $Y$
- $X+Y$ means $X$ is grandmother of $Y$

Statements:

- $V$\$A + B$
- $E & T$
- $C # S * T$
- $B @ H % C$\$E$

If $Z * H$, then who among the following is sister-in-law of $Z$?

Accepted Answer

**Solution:**

1. From the given notation:
   - $V$\$A + B$ means $V$ is spouse of $A$, and $A$ is grandmother of $B$.
   - $E & T$ means $E$ is father of $T$.
   - $C # S * T$ means $C$ is mother of $S$, and $S$ is sister of $T$.
   - $B @ H % C$\$E$ means $B$ is son of $H$, $B$ is daughter-in-law of $C$, and $C$ is spouse of $E$.

2. From $C # S * T$, $S$ and $T$ are siblings, and $C$ is their mother.

3. From $B @ H % C$\$E$, $B$ is son of $H$, and $B$ is daughter-in-law of $C$, so $B$ is married to $H$'s son. Since $C$ is mother of $S$ and $T$, and $B$ is daughter-in-law of $C$, $B$ must be married to either $S$ or $T$.

4. Given $Z * H$, $Z$ is sister of $H$.

5. The sister-in-law of $Z$ would be the wife of $Z$'s brother or the sister of $Z$'s spouse.

6. Since $Z$ is sister of $H$, $H$'s wife is $B$ (from above). So $B$ is sister-in-law of $Z$.

7. Also, $S$ is sister of $T$, and $S$ is daughter of $C$.

8. Since $B$ is daughter-in-law of $C$, $B$ is married to either $S$ or $T$'s brother, which is $H$.

9. Therefore, $S$ is sister-in-law of $Z$ because $S$ is sister of $H$ (Z's brother).

**Answer:** $S$

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