Correct Option:
Option 3 (Only four)
The relationships provided are:
- P is the brother of Q and R. This indicates P is male, and P, Q, R are siblings.
- S is R's mother. Consequently, S is also the mother of P and Q. S is female.
- T is P's father. Consequently, T is also the father of Q and R. T is male.
From these deductions, S and T are established as the parents of P, Q, and R, thereby forming a couple.
Evaluating each statement:
- Statement I: S and T are a couple. As S is the mother and T is the father of the same children (P, Q, R), they are a couple. This statement is definitely true.
- Statement III: T is Q's father. T is P's father, and Q is P's sibling. Therefore, T is also Q's father. This statement is definitely true.
- Statement IV: S is P's mother. S is R's mother, and P is R's sibling. Therefore, S is also P's mother. This statement is definitely true.
- Statement VI: P is S's son. P is identified as male (brother), and S is established as P's mother. Therefore, P is S's son. This statement is definitely true.
Thus, four statements (I, III, IV, VI) are definitely true.
Incorrect Options:
The following statements cannot be definitively concluded as true:
- Statement II: Q is T's son. While T is Q's father, Q's gender is not specified in the given information. Q could be either a son or a daughter. Therefore, this statement is not definitely true.
- Statement V: R is T's daughter. While T is R's father, R's gender is not specified in the given information. R could be either a son or a daughter. Therefore, this statement is not definitely true.
Options 1, 2, and 4 are incorrect as they do not accurately reflect the number of definitely true statements.