Question

{Months of a year whose names begin with the letter F } is:
(A) an infinite set
(B) empty set
(C) singleton set
(D) none of these

Answer 1

Hint: In order to this question, to know the type of set the given statement is, we will then explain the correct optional set and their properties. And then we will discuss more about the other type of set which is not correct.

Complete step-by-step solution:
Let $A = \{\text{months of a year whose name begin with the letter F}\} $
$ \Rightarrow A = \{\text{February}\} $
Therefore, it is a singleton set.
A singleton, also known as a unit group, is a set of exactly one element in mathematics. The set null, for example, is a singleton that contains the element null.
Singlet-based structures are often used as terminal objects or zero objects in a variety of categories: The statement above demonstrates that singleton sets are the category Set of sets' terminal objects.
The Singleton's job is to keep track of object formation and keep the number of objects to a minimum. Since there is only one Singleton instance, any instance fields of a Singleton, like static fields, will only appear once per class.
Hence, the correct option is (C).

Note: We can also say the singleton set as a unit set, as it contains only one element. As a result, in the category of sets, every singleton is a terminal entity. A singleton has the property of being injective to any arbitrary set of functions. The empty set is the only non-singleton set that has this property.