Select the set of classes whose relationship is best illustrated by the following diagram.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Even numbers, Multiples of 4, Multiples of 6
The diagram shows two overlapping circles, both inside a larger circle. So two classes must share some members, and both must lie wholly within the third class.
Option (1) Even numbers, Multiples of 4, Multiples of 6 — every multiple of 4 and every multiple of 6 is even, and 12 is a multiple of both, while 4 and 6 are not; two overlapping circles inside the even numbers, as in the diagram.
Option (2) Even numbers, Multiples of 4, Odd numbers — no odd number is even, so the odd-number circle stays apart from the even-number circle.
Option (3) Multiples of 2, Multiples of 4, Multiples of 8 — every multiple of 8 is a multiple of 4, which is a multiple of 2, so the circles lie one inside another.
Option (4) Even numbers, Odd numbers, Prime numbers — no number is both even and odd, so these two circles stay apart.
