The coded relations are as follows: B3D means B is the father of D, B7D means B is the sister of D, B2D means B is the brother of D and B1D means B is the wife of D. Which of the following expressions means that F is the mother of K?

Introduction / Context:
This is a symbolic blood relation question. Specific symbols represent simple family relations, and you need to find which combination of symbols expresses the idea that F is the mother of K. It checks your ability to decode and combine symbolic statements correctly.

Given Data / Assumptions:

• B3D means B is the father of D.
• B7D means B is the sister of D.
• B2D means B is the brother of D.
• B1D means B is the wife of D.
• We want an expression that shows F is the mother of K.
• A mother is a female parent, typically the wife of the father of a child.

Concept / Approach:
To show that F is the mother of K, we need to establish that F is female and that she is a parent of K. The symbols given allow us to show that someone is a father and that someone is a wife. The usual approach is to say that F is the wife of a man M, and that M is the father of K. That automatically makes F the mother of K.

Step-by-Step Solution:
Step 1: We want F to be female and a parent of K. The code B1D means B is the wife of D, so in an expression of the form F1M, F would be the wife (female spouse) of M.Step 2: To connect this to K, we can use the code B3D, which means B is the father of D. So M3K would mean M is the father of K.Step 3: Together, F1M3K reads as follows: F is the wife of M, and M is the father of K.Step 4: If M is the father of K and F is M wife, then F is the mother of K in a standard family structure.Step 5: Among the options, F1M3K is exactly this combination, so it represents F as the mother of K.

Verification / Alternative check:
Check the other options briefly. Expression F3M1K would start with F as the father of M, which already makes F male, not female, and then M as the wife of K, which is inconsistent. Expressions that include symbols like 9, 4 or 5 are not defined in the problem statement, so they cannot be interpreted correctly. Expression K3M4N5F is not meaningful under the given codes. Therefore, F1M3K is the only expression that decodes cleanly and matches the requirement that F is the mother of K.

Why Other Options Are Wrong:
Option a makes F the father, not the mother. Option b uses undefined symbols and does not give a clear meaning. Option c also uses undefined codes and puts F at the end in a way that cannot create a mother relation. Option e, M1F3K, would decode as M is the wife of F and F is the father of K, which would again make F male.

Common Pitfalls:
Students sometimes focus only on making F a parent of K and forget to ensure that F is female. Remember that both conditions are necessary for F to be the mother. Another common mistake is to read the expression in the wrong direction, but in these questions each pair such as F1M or M3K is read left to right according to the definitions given.

Final Answer:
The correct expression showing that F is the mother of K is F1M3K.