Select the Venn diagram that best illustrates the relationship between the following classes. Men, Engineers and Fathers
- (a)

- (b)

- (c)

- (d)

Answer
Why
Correct — A. Sort the three classes by what must be true of them.
Every father is a man, so the Fathers circle has to sit wholly inside the Men circle.
Engineers are not all men and not all fathers, yet some are both, so the Engineers circle must cut across the other two rather than sit inside or apart.
Option (a) draws exactly that: a small circle lying entirely within one large circle, with the second large circle overlapping both.
Why the others are wrong
- (b)Three separate circles say that no engineer is a man and no father is a man. A father is a man by definition, so total separation cannot be right.
- (c)A small circle inside a large one, plus a detached third circle. That third class touches nothing, but engineers and men do overlap, so no circle here may stand apart.
- (d)Two smaller circles sit side by side inside one big circle and never touch each other. That makes every engineer a man and denies that any father is an engineer.
Concept
A three-class Venn item asks for the one picture consistent with every relation among the classes, not merely a picture that is possible.
Test the pairs one at a time. Fathers and Men: a father is a male parent, so Fathers is a subset of Men and its circle goes inside.
Engineers and Men: some engineers are men and some are not, so those circles overlap partly. Engineers and Fathers: some engineers are fathers, so they overlap too.
Containment, partial overlap and separation are the only three pictures available, and each pair has to be assigned one of them.
The classes are everyday ones, so the deciding facts are definitional rather than factual: 'father' entails 'man', while 'engineer' entails neither.
Key facts
- A class wholly contained in another is drawn as a circle inside a circle.
- Two classes sharing only some members are drawn as two partly overlapping circles.
- Fathers is a subset of Men, because a father is a male parent.
- Engineers is not a subset of Men, so that circle can never sit wholly inside the Men circle.
Study next
Common traps
- Choosing a picture that is merely possible rather than the one that must hold
- Drawing Engineers inside Men because the engineers you can picture happen to be men
- Forgetting that Fathers, sitting inside Men, must also be cut by the Engineers circle
The classes are ordinary words, so the work is definitional and no outside knowledge is needed. The same containment-and-overlap reasoning decides the syllogism at Reasoning Q.12 of this shift, where three statements replace the picture.
Related PYQs
No directly related past PYQ was found.