Consider the following relationships among members of a family of six persons A, B, C, D, E and F: 1. The number of males equals that of females. 2. A and E are sons of F. 3. D is the mother of two, one boy and one girl. 4. B is the son of A. 5. There is only one married couple in the family at present. Which one of the following inferences can be drawn from the above?

Let's break down the relationships and deduce the family structure:

1. Persons: A, B, C, D, E, F (6 persons).
2. Gender Balance: Number of males = Number of females (3 males, 3 females).
3. A and E are sons of F: This means A is male, E is male. F is their parent.
4. B is the son of A: This means B is male.
   • So far, we have A (M), E (M), B (M). This accounts for all 3 males.
   • Therefore, the remaining persons C, D, F must be females (3 females).
   • From "A and E are sons of F" and F being female, F is the mother of A and E.
5. D is the mother of two, one boy and one girl: D is female. Since D is a mother, she must be part of the only married couple (from statement 5).
6. Only one married couple: This couple must consist of one male and one female.
   • From point 4, F is the mother of A and E.
   • From point 5, D is a mother.
   • B is the son of A. If D is the mother of B, then A (male) and D (female) must be the married couple. This fits the "only one married couple" condition.
   • If A and D are married, and D is the mother of two (one boy, one girl), then B (who is A's son) is their son. The other child must be a girl. The only remaining person is C (female). So, C is the daughter of A and D.

Family Structure Summary:

• Generation 1: F (Female) - Mother of A and E.
• Generation 2: A (Male) is married to D (Female). E (Male) is A's brother. (A and D are the only married couple).
• Generation 3: B (Male) and C (Female) are children of A and D.

Genders Check:

• Males: A, B, E (3 males) - Consistent.
• Females: C, D, F (3 females) - Consistent.

Now let's evaluate the options:

• A) A, B and C are all females: Incorrect. A is male, B is male, C is female.
• B) A is the husband of D: Correct. Our deduction shows A (male) and D (female) are the only married couple, with B and C as their children. This makes A the husband of D.
• C) E and F are children of D: Incorrect. E is D's brother-in-law (A's brother). F is D's mother-in-law (A's mother).
• D) D is the daughter of F: Incorrect. D is married to A, who is F's son. So D is F's daughter-in-law, not her daughter.

The final answer is B