let A be defined as the set of all two digit integers that are more than 20 and let P be defined as the set of all prime numbers .how many numbers are there that belong to both these sets?
1.13
2.17
3.21
4.25
explain the ans please
You are probably just as good as googling and counting as I am
Goggle a list of primes.
count how many primes you see from 23 to 97
the ans is 17..
To find the numbers that belong to both sets A and P, we need to identify the prime numbers within the set of two-digit integers greater than 20.
To find the prime numbers within the set A, we can start by listing all two-digit integers greater than 20:
21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39,
...
and so on.
Next, we need to identify which of these numbers are prime. A prime number is a number greater than 1 that only has two positive divisors: 1 and itself.
Using this definition, we can identify the prime numbers within set A:
23, 29,
31, 37,
...
and so on.
Now, let's look at the options given:
1. 13: While 13 is a prime number, it does not belong to set A because it is not a two-digit integer greater than 20.
2. 17: Similar to 13, 17 is a prime number, but it does not belong to set A for the same reason.
3. 21: 21 is a two-digit integer greater than 20, but it is not a prime number because it is divisible by 3.
4. 25: 25 is also a two-digit integer greater than 20, but it is not a prime number because it is divisible by 5.
So the correct answer is 0, as there are no numbers that belong to both sets A and P.