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

Answer

To classify the set of prime numbers less than one crore, we will follow these steps:

### Step 1: Understand the Definition of Prime Numbers
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, a prime number has exactly two distinct positive divisors: 1 and itself.

**Hint:** Remember that prime numbers start from 2, and the smallest prime number is 2.

### Step 2: Identify the Range
The question specifies that we are looking for prime numbers that are less than one crore. One crore is equal to 10,000,000.

**Hint:** Think about how many numbers are there from 1 to 10,000,000.

### Step 3: Count the Prime Numbers Less Than One Crore
There are known algorithms and methods to find prime numbers within a certain range. It has been established that there are 664579 prime numbers less than 10,000,000.

**Hint:** You can use the Sieve of Eratosthenes or other methods to find the count of prime numbers in a range.

### Step 4: Determine if the Set is Finite or Infinite
Since we have counted the prime numbers and found that there are 664579 of them, we can conclude that the set of prime numbers less than one crore has a specific number of elements.

**Hint:** A set is finite if it contains a specific count of elements.

### Step 5: Classify the Set
Based on the above analysis, we can classify the set of prime numbers less than one crore as a finite set because it contains a specific number of elements (664579).

**Final Answer:** The set of prime numbers less than one crore is a **finite set**.