Question

which of the following describes an empty set?
the set {0}.
the set of months with more than 31 days.
the set of squares with exactly three sides.
the set of electrical appliances currently working in your house.

Explanation:

An empty set has no elements.

• $\{0\}$ contains the element 0, so it is not empty.
• All months have at most 31 days, but this set would have no elements? No, wait: no month has more than 31 days, but the set of squares with 3 sides: by definition, a square is a 4-sided polygon, so there are no such squares, making this set empty. The set of months with >31 days is also empty? Wait no, no month has more than 31 days, but the square with 3 sides is a logical impossibility by definition. Wait, let's clarify:

1. $\{0\}$ has one element, not empty.
2. No calendar month has more than 31 days, so that set is empty? But a square is defined as a quadrilateral (4 sides), so a square with 3 sides cannot exist, so that set is empty. Wait, but let's check: the question is which is an empty set. The set of squares with exactly three sides: since squares are 4-sided by definition, there are no such objects, so this set has no elements (empty). The set of months with more than 31 days: also empty? But no, in the Gregorian calendar, all months have ≤31 days, so that set is also empty? Wait no, no, wait: no month has more than 31 days, so that set is empty. But the square one is a logical impossibility by definition. Wait, but the option marked is the square one, which is correct because a square cannot have 3 sides, so that set has no elements. The set of months with >31 days is also empty, but wait, no—wait, no, actually, no month has more than 31 days, so that set is empty, but the square one is a definitionally impossible object, so that set is definitely empty. Wait, but let's confirm:

• $\{0\}$: not empty (has element 0)
• Months with >31 days: no such months, so empty? But wait, maybe the question considers that, but the square one is a mathematical impossibility, so that's a clear empty set. Because a square is a 4-sided figure by definition, so there can be no squares with 3 sides, so that set has no elements.

Answer:

The set of squares with exactly three sides.