Question

Classify the following sets as empty set, finite set or infinite set:
The set of prime numbers is less than one crore.

Answer 1

Hint: We solve this question by converting to the given roaster form for the above statement. Then we need to determine whether the set has a countable number or elements or not. If it has no elements, it is said to be a null set. If it has a finite number of elements then it is a finite set else it is an infinite set.

Complete step by step answer:
In order to solve this question, let us first understand the concept of finite and infinite sets. A set is said to be a finite set if there exists a finite number of elements within the set. They are also called countable sets. On the other hand, we have infinite sets which contain an infinite or uncountable number of elements within them. This cannot be represented in roaster form due to the number of elements being infinite. A null set is a set that contains no elements at all. This means that a null set has zero elements.
The given statement says we have a set containing elements that are prime numbers less than one crore. Firstly, we have a finite number of elements from 1 to one crore. Also, prime numbers are numbers that are positive which are divisible only by one and itself. This set is represented in roaster form as $\left\{ 2,3,5,7,11,13,\ldots \ldots 9999991 \right\}$ . Since there are countably many elements in this set, it is a finite set.
Hence, the set of prime numbers less than one crore is a finite set.

Note: We need to know the concept of sets in order to solve such sums. We need to be careful while considering the prime numbers because the prime numbers are all positive numbers. If we were given a set of, say integers, it could be negative also and since the lower limit is not specified, it would have been an infinite set.