P is the brother of Q and R. S is R’s mother. T is P’s father. How many of the following statements are definitely true?
I. S and T are a couple. II. Q is T’s son.
III. T is Q’s father. IV. S is P’s mother.
V. R is T’s daughter. VI. P is S’s son.
Select the correct answer using the code given below:

The correct option is Only four.

Step-by-step Explanation:

Let us analyze the relationships given in the problem statement:

1. P is the brother of Q and R: This means P is a male, and P, Q, and R are siblings (they share the same parents).

2. S is R’s mother: Since P, Q, and R are siblings, S must be the mother of all three children (P, Q, and R).

3. T is P’s father: Since P, Q, and R are siblings, T must be the father of all three children (P, Q, and R).

4. From (2) and (3), since S is the mother and T is the father of the same children, S and T are married to each other, forming a couple.

Now, let us evaluate the gender information:

- P: Male (since P is the brother of Q and R).

- Q: Gender is not specified (can be male or female).

- R: Gender is not specified (can be male or female).

- S: Female (Mother).

- T: Male (Father).

Let us evaluate each of the given statements to check if they are definitely true:

I. S and T are a couple.

Since S is the mother and T is the father of P, Q, and R, S and T are married/a couple. (Definitely True)

II. Q is T’s son.

Q is a child of T, but Q's gender is unknown (could be son or daughter). (Not definitely true)

III. T is Q’s father.

T is the father of P, Q, and R, so T is definitely Q's father. (Definitely True)

IV. S is P’s mother.

S is the mother of R, and P is R's sibling, so S is definitely P's mother. (Definitely True)

V. R is T’s daughter.

R is a child of T, but R's gender is unknown (could be son or daughter). (Not definitely true)

VI. P is S’s son.

P is male (brother of Q and R) and S is his mother, so P is definitely S's son. (Definitely True)

Conclusion:

The statements that are definitely true are I, III, IV, and VI. Thus, exactly four statements are definitely true.