Select the Venn diagram that best represents the relationship between the…
2023
Select the Venn diagram that best represents the relationship between the following classes.
Snakes, Crocodiles, Reptiles
Attempted by 4 students.
Show answer & explanation
Concept
In a logical Venn diagram the way two regions are drawn fixes the relationship between the classes they stand for. A region drawn wholly inside another region means every member of the inner class is also a member of the outer class. Two regions that partly overlap mean the two classes share some of their members but not all. Two regions drawn apart, with no common area, mean the two classes share no member at all.
Application
Apply those three readings to Snakes, Crocodiles and Reptiles:
Every snake is a reptile, so the region standing for snakes must lie completely inside the region standing for reptiles.
Every crocodile is a reptile, so the region standing for crocodiles must also lie completely inside the region standing for reptiles.
No snake is a crocodile and no crocodile is a snake, so the snake region and the crocodile region must share no area at all.
Combining the three requirements, the picture must be one large region holding two smaller regions that stay clear of each other.
Cross-check
Testing each drawn structure against those three requirements:
Structure drawn | Relationship it asserts | Fit with the three classes |
|---|---|---|
One large circle enclosing two smaller circles that do not touch | Two classes lie wholly inside a third and share no member with each other | Meets all three requirements |
Two partly overlapping circles beside a separate circle | Two classes share some members; a third shares none with either | Snakes and crocodiles share no member, and both lie inside reptiles, so this does not fit |
Three circles in a row, each overlapping its neighbour | Neighbouring classes share only part of their members | Snakes and crocodiles lie wholly, not partly, inside reptiles, so this does not fit |
A small circle inside a larger circle, that larger circle overlapping a third | One class lies inside a second; the second only partly meets a third | It leaves one of the two animal classes only partly inside reptiles, so this does not fit |
Result
The diagram that best represents Snakes, Crocodiles and Reptiles is therefore the one showing a single large circle that encloses two smaller circles which do not touch each other.