'D ≡ G’ means ‘D is the sister of G’. ‘D ∆ G’ means ‘D is the husband of G’. ‘D ∇ G’ means ‘D is the daughter of G’. ‘D ∃ G’ means ‘D is the mother of G’. ‘D ∞ G’ means ‘D is the brother of G’. Which of the following expressions denotes that ‘S is the husband of M’?
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'.
| Option | Expression Breakdown | Relationship between S and M |
|---|---|---|
| 1 | S is brother of H, H is sister of L, L is sister of Q, Q is mother of M | S is M's maternal uncle |
| 2 | Q is daughter of M, M is mother of H, H is sister of L, L is mother of S | M is S's maternal grandmother |
| 3 | M is mother of Q, Q is husband of L, L is sister of H, H is mother of S | M is S's maternal grand-aunt |
| 4 | M is mother of Q, Q is sister of L, L is brother of H, H is daughter of S | S is the husband of M |
Revision Table: Key Blood Relations and Symbols
| Symbol | Relation | Example (D Relation G) | Gender Implied (D) | Gender Implied (G) |
|---|---|---|---|---|
| $\equiv$ | Sister of | D is the sister of G | Female | Sibling (Male/Female) |
| $\Delta$ | Husband of | D is the husband of G | Male | Female |
| $\nabla$ | Daughter of | D is the daughter of G | Female | Parent (Male/Female) |
| $\exists$ | Mother of | D is the mother of G | Female | Child (Male/Female) |
| $\infty$ | Brother of | D is the brother of G | Male | Sibling (Male/Female) |
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.
Important Questions from Coded Blood Relation Problems
‘A # B’ means ‘A is the son of B’.
‘A @ B’ means ‘A is the mother of B’.
‘A & B’ means ‘A is the wife of B’.
‘A % B’ means ‘A is the sister of B’.
If ‘M @ R % K # G # N & T’, then which of the following statements is NOT correct?
‘A % B’ means ‘A is the sister of B’.
‘A $ B’ means ‘A is the brother of B’.
‘A @ B’ means ‘A is the son of B’.
‘A & B’ means ‘A is the mother of B’.
If ‘R % T & Z $ S @ V @ C % Y’, then which of the following statements is NOT correct?
Read the given information carefully and answer the question that follows.
‘K $ D’ means ‘K is the father of D’.
‘K < D’ means ‘K is the wife of D’.
‘K > D’ means ‘K is the daughter of D’.
'K @ D’ means ‘K is the son of D’.
How is S related to N in the expression ‘H > R $ S @ T > N’?
‘R8S’ means ‘R is the father of S’.
‘R7S’ means ‘R is the sister of S’.
‘R6S’ means ‘R is the brother of S’.
‘R2S’ means ‘R is the wife of S’.
Which of the following expressions represents ‘X is the mother of Y’?
‘A # B’ means ‘A is the father of B’.
‘A % B’ means ‘A is the mother of B’.
‘A @ B’ means ‘A is the sister of B’.
‘A & B’ means ‘A is the son of B’.
If ‘G # M # T % S @ H & R & W @ U’, then which of the following statements is NOT correct?
