Question

Read the information given below and answer the questions that follow-
(J) If P + Q means; P is the brother of Q.
(K) P \(\times\) Q means; P is the father of Q; and
(L) P \(-\) Q means; P is the sister of Q.
Then, which of the following represents S is the niece of T?

• A. T \(\times\) M + S \(-\) K
• B. K \(-\) S \(\times\) M + T
• C. T + M \(\times\) S \(-\) K
• D. T \(\times\) S + M \(-\) K

Hint:

Always apply gender elimination first! Since "niece" is female, look at the symbol immediately following 'S'. S must be followed by '-' (sister) to be female. This immediately eliminates options B and D.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to find the coded expression representing "S is the niece of T". "Niece" means S must be female, and her parent must be a sibling of T.

Step 2: Detailed Explanation:
Let us translate the family relationships of the options:
- Gender Constraint: Since S is a niece, S must be female.
- In (B): \( S \times M \) means S is the father of M. Thus, S is male, which is incorrect.
- In (D): \( S + M \) means S is the brother of M. Thus, S is male, which is incorrect.
This leaves options (A) and (C). Let's evaluate them:
- Option (A): \( T \times M + S - K \)
- \( T \times M \): T is the father of M.
- \( M + S \): M is the brother of S.
- \( S - K \): S is the sister of K.
Since T is the father of M, and M is the sibling of S, T must be the father of S. Thus, S is the daughter of T, not the niece. So Option (A) is incorrect.
- Option (C): \( T + M \times S - K \)
- \( T + M \): T is the brother of M.
- \( M \times S \): M is the father of S.
- \( S - K \): S is the sister of K (which confirms S is female).
Since M is the father of S, and T is the brother of M, T is the paternal uncle of S. Since S is female, S is indeed the niece of T.
Thus, Option (C) represents "S is the niece of T".

Step 3: Final Answer:
(C) T + M \(\times\) S \(-\) K