Assume set A contains all even numbers, set B contains all prime numbers, and set C contains all numbers divisible by 3; identify the elements common to all three sets within the range of 1 to 100.
user
Sure, I can help you with this. So, there are only two even prime numbers within the range of 1 to 100, which are 2 and 3. Therefore, if you assume set A as "all even numbers" and set B as "all prime numbers" and set C as "all numbers divisible by 3", the common element is 6, which is even, prime and divisible by 3.

Now, to answer your question solves the problem in a different way; let's consider:

- Set A contains all even numbers (2, 4, 6, 8, 10, ..., 98, 100)
- Set B contains all prime numbers (2, 3, 5, 7, 11, ..., 67, 71, 73, 79, 83, 89, 97)
- Set C contains all numbers divisible by 3 (3, 6, 9, 12, ..., 99, 102)

Then, the common elements are 6, which satisfies all three properties at once.

Therefore, The elements present in all three sets simultaneously is (6).
assistant
Assume set A contains all even numbers, set B contains all prime numbers, and set C contains all numbers divisible by 3; identify the elements common to all three sets within the range of 1 to 100.
user
To find the elements common to all three sets within the range of 1 to 100, we need to look for numbers that are even, prime, and divisible by 3.

However, there is a contradiction in the criteria. Prime numbers are numbers greater than 1 that have only two factors: 1 and the number itself. The only even prime number is 2, and 2 is not divisible by 3. Therefore, there are no numbers that can satisfy all three conditions simultaneously.

So, there are no elements common to all three sets (A, B, and C) within the range of 1 to 100.
assistant