Decoding Blood Relation Puzzles

This problem involves understanding coded language for blood relations and then building a family tree based on the given expression to determine the relationship between two individuals.

Understanding the Coded Relations

The question provides the following code:

• A - B means A is father of B
• A + B means A is mother of B
• A × B means A is husband of B
• A $\div$ B means A is the son of B

Analyzing the Given Expression: U $\div$ Q $\div$ P - R $\times$ S + T $\times$ V

Let's break down the expression segment by segment, from left to right, to build the relationships:

• U $\div$ Q: Using the rule 'A $\div$ B' means 'A is the son of B', this means U is the son of Q. (Q is U's parent, gender of Q is not yet known from this part).
• Q $\div$ P: Using the rule 'A $\div$ B' means 'A is the son of B', this means Q is the son of P. (P is Q's parent, gender of P is not yet known from this part). Since Q is the son of P, P is the father or mother of Q. Since U is the son of Q, U is the grandson of P.
• P - R: Using the rule 'A - B' means 'A is father of B', this means P is the father of R. (P is male). We know P is a parent of Q, and Q is P's son. So P is Q's father. Since P is also the father of R, Q and R are siblings.
• R $\times$ S: Using the rule 'A × B' means 'A is husband of B', this means R is the husband of S. (R is male, S is female). R and S are a married couple.
• S + T: Using the rule 'A + B' means 'A is mother of B', this means S is the mother of T. (S is female).
• T $\times$ V: Using the rule 'A × B' means 'A is husband of B', this means T is the husband of V. (T is male, V is female). T and V are a married couple.

Building the Family Tree and Finding the Relation between U and V

Let's trace the connections starting from V to reach U:

• V is married to T. So, T is V's husband.
• S is the mother of T. So, S is V's husband's mother (V's mother-in-law).
• R is the husband of S. Since S is T's mother and R is S's husband, R is T's father. R is V's husband's father (V's father-in-law).
• P is the father of R. Since R is T's father and P is R's father, P is T's grandfather (V's husband's father's father).
• Q is the son of P. Since P is the father of R and also the father of Q (and Q is his son), Q is R's brother. R is T's father, so Q is T's father's brother. T is V's husband, so Q is V's husband's father's brother.
• U is the son of Q. Since Q is V's husband's father's brother, U is the son of V's husband's father's brother.

Therefore, U is the son of V's husband's father's brother.

Evaluating the Options

Let's compare our derived relationship with the given options:

1. Husband's father's brother: This describes Q, not U.
2. Husband's father's father: This describes P, not U.
3. Father-in-law: This describes R, not U.
4. Son of husband's father's brother: This matches our derived relationship for U.

Based on the detailed analysis of the coded relations and the expression, the relationship between U and V is that U is the son of V's husband's father's brother.