Which diagram best represents the relationship among Doctor, Women, and Mother?
2013
Which diagram best represents the relationship among Doctor, Women, and Mother?
Show answer & explanation
In a class-relationship (Venn) diagram, the way two circles are drawn encodes the logical connective between the categories: a universal statement ("every A is B") forces circle A entirely inside circle B; a partial-overlap statement ("some A are B", with also "some A are not B" and "some B are not A") forces the two circles to intersect without either containing the other; and when a third category relates to both groups by such "some" statements on each side, its circle must cross into both regions at once.
“Every mother is a woman” is a universal statement, so the Mother circle must sit entirely inside the Women circle.
“A doctor can be male or female” means Doctor and Women only partly overlap — the Doctor circle must also extend outside the Women circle.
“Some mothers are doctors” means the Doctor circle must also cut into the Mother circle, not just the outer Women region.
Combining all three: the required diagram places a small circle (Mother) wholly inside a larger circle (Women), with a third circle (Doctor) crossing through both the Mother and the Women regions while also extending outside them.
Checking against each incorrect diagram confirms this is the only consistent option:
Two separate, non-touching circles inside a third circle would mean no mother is a doctor and every doctor is a woman — this contradicts both “some mothers are doctors” and “a doctor may be a man.”
Three fully separate circles with no overlap at all would mean no woman is a mother and no woman is a doctor — this contradicts “every mother is a woman” and the fact that many women are doctors.
Two overlapping circles placed entirely inside an outer circle would confine every doctor within the women group, leaving no doctor outside it — this contradicts “a doctor may also be a man.”
So the only diagram consistent with all three facts is the one with the small circle (Mother) wholly inside the larger circle (Women), crossed by a third circle (Doctor).