Question

Identify the type of set: A = { x : x is neither prime nor composite}
A. Empty Set
B. Singleton Set
C. Infinite Set
D. Finite Set

Answer 1

We will first find out the elements in the set which we need to identify and then we will just calculate the number of elements in the set and then classify as required.

Complete step-by-step answer:
We have to identify the set: A = { x : x is neither prime nor composite}
Here, we have to select such numbers which are neither prime nor composite.
Now, since any number we pick up is either prime or composite except 1 which is called a unit digit.
1 is neither prime nor composite.
So, we have A = {1}
We can clearly see that A has only one element, therefore, it is a singleton set.

Hence, the correct option is (B).

Note:
The students must know the definition or prime and composite numbers so that they can find the elements of the set easily.
Prime Number: The natural numbers which have only 1 and itself as the factors are known as prime numbers.
Composite Numbers: The natural numbers which are not prime are known as composite numbers.
Now, 1 has the factor of 1 only, so it does not fall under any of the categories, so it is neither prime nor composite.
The students must also know the difference in the following sets which are given as options in the above question:-
Empty Set: The set which has no elements is called an empty set or null set.
For example: A = {x : x is a natural number greater than 1 but less than 2}
Singleton Set: The set which contains only one element is known as a singleton set.
For example: B = {x : x is a natural number greater than 1 but less than 3} = {2}
Infinite Set: The set which contains an infinite number of elements.
For example: C = {x : x is a natural number}
Finite Set: The set which has a finite number of elements.
For example: D = {1, 2, 3, 4, 5, 6, 7}