Select the Venn diagram that best represents the relationship among the…
2019
Select the Venn diagram that best represents the relationship among the following sets: Pluto, Moon, Mars, Solar System.
Attempted by 208 students.
Show answer & explanation
Concept
In a Venn diagram, how the circles are drawn encodes the logical relationship between the sets. One circle drawn completely inside another shows a subset relationship, where every member of the inner set is also a member of the outer set. Several circles drawn separately from each other but placed inside one large circle show mutually independent items that are each, individually, members of one larger common category, with no subset relationship among themselves. A circle drawn outside the large circle shows an item that is not a member of that category.
Application
The four named sets here are Pluto, the Moon, Mars, and the Solar System. The Moon is a natural satellite of Earth, so it is not a satellite of Mars or Pluto and cannot be nested inside either of them. Mars is a planet and Pluto is a dwarf planet in the outer Solar System; neither is a subset of the other or of the Moon. Pluto and Mars orbit the Sun directly, and the Moon orbits Earth as part of the Earth–Moon system, which itself orbits the Sun; all three are therefore members of the Solar System, which acts as the encompassing category here.
Contrast
A diagram with one circle drawn completely inside another would wrongly claim that one of these three items is a subset of another, which does not hold since none of the three is contained within any other.
A diagram with three concentric, chain-nested circles would wrongly claim a chain of containment running through all three items, which likewise does not hold since they are mutually independent.
A diagram that places one of the three items outside the large Solar-System circle would wrongly claim that item is not part of the Solar System, but Pluto, the Moon, and Mars are all Solar System members.
Answer
The correct representation is one large circle for the Solar System containing three separate, non-overlapping small circles, one each for Pluto, the Moon, and Mars, since all three are independent members of the Solar System with no subset relationship among them.