I. A, B, C, D, E and F are six members of a family. II. One couple has their parents and their children also included in the family. III. A is the son of C and E is the daughter of A. IV. D is the daughter of F, who is the mother of E. How many female members are there in the family?

Introduction / Context:

This is a logical family-structure puzzle where you must use several clues about parents, children and one specific couple to determine how many female members are in the family. It tests your ability to combine information about gender (son, daughter, mother) and roles (parents, couple) and to distinguish between what is definitely known and what is not explicitly given.

Given Data / Assumptions:

• There are six family members: A, B, C, D, E and F.
• One married couple is present along with their parents and their children in this family.
• A is the son of C.
• E is the daughter of A.
• D is the daughter of F, and F is the mother of E.
• We assume standard gender meanings: "son" and "father" are male; "daughter" and "mother" are female.
• We need to count how many members are definitely female.

Concept / Approach:

The strategy is to identify each person's gender where it is clearly specified, and to see whether any additional gender information can be safely inferred. A is described as a son (male) and F as a mother (female). E and D are both described as daughters (female). C and B are not explicitly labeled as male or female in the statements. While the structure hints at possible parent roles for B and C, we only count those whose gender is clearly specified or strongly implied by words like "mother" or "daughter".

Step-by-Step Solution:

Verification / Alternative check:

Try to assign genders to B and C in different ways. In one scenario, C might be A's father (male) and B might be F's father (male). In another scenario, C might be A's mother (female) and B might be F's father (male). Both scenarios are consistent with the clues and still keep three females (F, E, D) definitely female. Because the puzzle does not force C or B to be female, the only guaranteed female count is three.

Why Other Options Are Wrong:

"2" is too low, because F (mother) and at least one daughter (E or D) are clearly female, and we also have a second daughter, giving at least three females.

"4" or "5" would require us to assume that C and/or B are definitely female, but the statements simply do not supply that information. Making such assumptions would go beyond the text.

Common Pitfalls:

A common mistake is to overinterpret "one couple has their parents and their children in the family" and assume exact genders for B and C (for example, forcing C to be the father and B to be the grandmother). However, without explicit words like "father" or "grandmother", such assumptions are not guaranteed. In exam-style logic problems, only count genders that are clearly indicated by terms like son, daughter, mother or father.

Final Answer:

There are exactly 3 female members in the family: F, D and E.