Analyzing Blood Relation Expressions

This question asks us to identify which given expression represents the relationship 'S is the husband of M' based on a defined set of symbolic relationships.

Let's first understand the meaning of each symbol:

• $\text{D} \equiv \text{G}$: D is the sister of G
• $\text{D} \Delta \text{G}$: D is the husband of G
• $\text{D} \nabla \text{G}$: D is the daughter of G
• $\text{D} \exists \text{G}$: D is the mother of G
• $\text{D} \infty \text{G}$: D is the brother of G

We are looking for an expression where S is the husband of M. This means M is the wife of S.

Evaluating Each Expression for S as Husband of M

Option 1: S $\infty$ H $\equiv$ L $\equiv$ Q $\exists$ M

Let's break down this expression step by step:

• S $\infty$ H: S is the brother of H. (S is Male)
• H $\equiv$ L: H is the sister of L. (H is Female, H and L are siblings)
• L $\equiv$ Q: L is the sister of Q. (L is Female, L and Q are siblings)
• Q $\exists$ M: Q is the mother of M. (Q is Female, M is her child)

From the first three parts, S, H, L, and Q are siblings. S is male, H, L, and Q are female. Q is the mother of M. This means S is the brother of Q's child's mother. So, S is M's maternal uncle. This expression does not mean S is the husband of M.

Option 2: Q $\nabla$ M $\exists$ H $\equiv$ L $\exists$ S

Let's break down this expression:

• Q $\nabla$ M: Q is the daughter of M. (Q is Female, M is her parent)
• M $\exists$ H: M is the mother of H. (M is Female, H is her child)
• H $\equiv$ L: H is the sister of L. (H is Female, H and L are siblings)
• L $\exists$ S: L is the mother of S. (L is Female, S is her child)

From Q $\nabla$ M and M $\exists$ H, M is the mother of Q and H. H and L are siblings (H is sister of L). So M is also the mother of L. Thus, M is the mother of Q, H, and L. L is the mother of S. This makes M the mother of S's mother, meaning M is S's maternal grandmother. This expression does not mean S is the husband of M.

Option 3: M $\exists$ Q $\Delta$ L $\equiv$ H $\exists$ S

Let's break down this expression:

• M $\exists$ Q: M is the mother of Q. (M is Female, Q is her child)
• Q $\Delta$ L: Q is the husband of L. (Q is Male, L is his wife - Female)
• L $\equiv$ H: L is the sister of H. (L is Female, H is her sibling)
• H $\exists$ S: H is the mother of S. (H is Female, S is her child)

M is the mother of Q. Q is the husband of L. L and H are sisters. H is the mother of S. This means M is the mother of L's husband. L is H's sister. H is S's mother. Q is L's husband. H is L's sister, so Q is H's brother-in-law. H is S's mother. Q is S's maternal uncle. M is Q's mother, so M is S's maternal grand-aunt. This expression does not mean S is the husband of M.

Option 4: M $\exists$ Q $\equiv$ L $\infty$ H $\nabla$ S

Let's break down this expression step by step, working from right to left to connect M and S:

• H $\nabla$ S: H is the daughter of S. (H is Female, S is her parent)
• L $\infty$ H: L is the brother of H. (L is Male, L and H are siblings)
• Q $\equiv$ L: Q is the sister of L. (Q is Female, Q and L are siblings)
• M $\exists$ Q: M is the mother of Q. (M is Female, Q is her child)

Combining the sibling relationships: Q is the sister of L, and L is the brother of H. This means Q, L, and H are siblings. Q is female, L is male, and H is female (since H is the daughter of S). M is the mother of Q. Since Q, L, and H are siblings, M must be the mother of L and H as well. M is female.

Now consider H $\nabla$ S: H is the daughter of S. We know M is the mother of H, and H is also the daughter of S. For H to have two parents, one is the mother (M) and the other must be the father (S). Therefore, S is the father of H. Since S is the father and M is the mother of the same child (H), S and M must be married, and S is the husband of M (as S is male, father).

This expression successfully denotes that 'S is the husband of M'.

Conclusion

By analyzing each expression based on the given blood relation codes, we found that Option 4 correctly represents 'S is the husband of M'.

Revision Table: Key Blood Relations and Symbols

Additional Information on Solving Blood Relation Problems

Solving blood relation problems with codes involves translating the symbols into standard relationships and then constructing a family tree or diagram to visualize the connections. Here are some tips:

• Read the instructions carefully to understand what each symbol represents.
• Note down the gender implied by each relationship for the first person (e.g., 'is the husband of' means the first person is male).
• Break down complex expressions into smaller, two-person relationships.
• Build a family tree diagram. Use different shapes or symbols for males and females (e.g., circle for female, square for male) and lines to show relationships (vertical for parent-child, horizontal for siblings, double horizontal for marriage).
• Evaluate the resulting relationships between the individuals mentioned in the question (S and M in this case).
• Work through each option systematically until you find the one that matches the target relationship.

These problems test your ability to decode information and logically deduce relationships within a family structure.