Which figure best represents the relation among Fathers, Teacher, Males?

Question

Which figure best represents the relation among Fathers, Teacher, Males?

1. A. (Correct answer)
2. B.
3. C.
4. D.

Correct Answer

Option A — A small circle lying entirely inside a larger circle, with a third circle overlapping both of them and extending outside the larger circle.

Detailed Solution & Explanation

The correct answer is option A.

Key Points

• Take the three classes one relation at a time:
  • Fathers and Males — every father is a man, and there is no father who is not male. The Fathers circle therefore lies wholly inside the Males circle.
  • Teachers and Males — some teachers are men and some are women, so the Teachers circle partly overlaps Males and also reaches outside it.
  • Teachers and Fathers — a teacher may be a father and a father may be a teacher, but neither follows from the other, so these two circles overlap partly as well.
• The diagram that satisfies all three at once is a small circle inside a larger circle, with a third circle cutting across both and spilling outside — which is option A.

Additional Information

• The deciding test is containment versus overlap. "Every A is B" is the only relation that nests one circle inside another; anything weaker is an overlap. Sorting the pairs into those two buckets before looking at the options is faster than comparing pictures.
• Option B makes all three classes mutually overlapping, which wrongly allows a father who is not male.
• Option C strings the circles in a row so that Fathers merely overlaps Males, again permitting a non-male father.
• Option D puts Fathers and Teachers inside Males as two separate circles. That commits two errors: it makes every teacher male, and it makes it impossible for a teacher to be a father.
• Read the classes as sets of people, not as jobs and roles. Candidates lose this question by reasoning that "a father cannot be a teacher at the same time", which confuses a person's two attributes with two disjoint groups.