Let's check the logical connection in option (a):
Statement A: Mary is John’s wife.
Statement D: Husband and wives danced the last waltz.
Statement F: John danced last with Mary.
From A and D, we establish that Mary and John (being husband and wife) are among those who danced the last waltz.
From F, we know that John danced last with Mary — consistent with A and D.
Hence, all three statements are tightly linked and logically reinforce each other.
Now check the other options for completeness:
Option (b) ABD:
- A and D are valid together.
- But B (Mary and John danced together) is very general and doesn’t necessarily connect with D (about dancing the last waltz). So B does not strongly link with D or A.
Option (c) ACE:
- A: Mary is John’s wife.
- C: Mary wears John’s ring — this is a weak implication of being his wife but not definitive.
- E: John loves Mary — again, not necessarily connected with the marriage or dancing context.
Logical link is weak.
Option (d) AEF:
- A: Mary is John’s wife.
- E: John loves Mary — valid.
- F: John danced last with Mary — fits, but E is emotionally descriptive, not action-based.
This is logically acceptable but slightly less tightly structured than ADF.
Conclusion: ADF is the most logically coherent and contextually consistent set.