Hi. I found this question on a Math Counts practice test and it seriously confused me. I've never learned about this, and it would help if someone helped me. Thanks in advance.
How many elements are in the intersection of the set of all the prime numbers less than 30 and the set of all the odd numbers greater than zero?
Problems
1. I don't even understand the question.
2. What does the question mean by elements?
3. Pleas don't just give me the answer, because I really want to know how to solve these types of questions in case it appears later on.
No problem! Let's break down the question and go step-by-step:
1. Understanding the question:
The question is asking how many elements (or numbers) are common to both sets: the set of all prime numbers less than 30 and the set of all odd numbers greater than zero.
2. What does the question mean by elements?
In this context, elements refer to the individual numbers that make up the sets.
Now, let's move on to solving the problem:
To find the solution, we need to determine the prime numbers less than 30 and the odd numbers greater than zero. Then, we'll find the common numbers in both sets and count them.
Step 1: Prime Numbers less than 30:
The prime numbers less than 30 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Step 2: Odd numbers greater than zero:
Since we are looking for odd numbers greater than zero, all positive integers that are not divisible by 2 are considered. So, the odd numbers greater than zero are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, and 29.
Step 3: Finding the intersection (common numbers):
By looking at both sets, we can see that the common numbers are: 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Step 4: Counting the common numbers:
To count the number of elements in the intersection, we simply count the common numbers we found in Step 3. In this case, there are 9 common elements.
Therefore, the answer to the given question is: There are 9 elements in the intersection of the set of all prime numbers less than 30 and the set of all odd numbers greater than zero.
I hope this explanation helps you not only with this question but also in tackling similar types of problems in the future!
First, brush up the notion of sets. For example:
http://en.wikipedia.org/wiki/Set_%28mathematics%29
The intersection of two sets A and B is written as:
A∩B
Set A could be defined as :{1,2,3,4,5}
and set B could be defined as:{2,4,6,8,10)
The intersection of sets A and B, A∩B, is another set containing members which are present in both A and B, namely A∩B={2,4}.
So whis is the intersection of the set of primes less than 30,
P={2,3,5,7,11,13,17,19,23,29}
and the set of all positive odd numbers,
Q={1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,....ad infinitum}
So what is P∩Q?
Post what you think.
Hey there! Don't worry, I'm here to help you with this question. Let's break it down step by step and make sense of it.
1. The question is asking about the "intersection" of two sets. In mathematics, the intersection of two sets is the collection of elements that are common to both sets.
2. In this case, the two sets we are dealing with are:
- The set of all prime numbers less than 30
- The set of all odd numbers greater than zero
3. Now, an "element" refers to the individual items within a set. For example, in a set of {1, 2, 3, 4}, the elements would be 1, 2, 3, and 4.
To solve this question, you need to find the numbers that are both prime and odd. Think about it this way: odd numbers are those that can't be divided evenly by 2, and prime numbers are those that have only two distinct positive divisors (1 and themselves).
Now, you can list out the prime numbers less than 30 and the odd numbers greater than zero separately, and then find the common ones. Or, if you are familiar with the concept of prime numbers, you can determine the common prime numbers among odd numbers greater than zero.
Once you find the common prime numbers among the odd numbers greater than zero, count how many there are, and that will give you the number of elements in the intersection.
Remember, it's always good to have a firm grasp on the definitions and concepts involved in a question before attempting to solve it. Don't hesitate to reach out if you have more questions!
Hi! I'd be happy to help you understand and solve this question.
1. Understanding the question:
The question is asking about the "intersection" of two sets. In mathematics, the intersection of two sets refers to the elements that are common to both sets. To solve this problem, we need to find the numbers that are both prime and odd within specific ranges.
2. Understanding "elements":
In the context of this question, "elements" refer to the individual numbers that belong to the sets. For example, in the set of prime numbers less than 30, the elements are the prime numbers within that range.
Now let's move on to solving the problem step-by-step:
Step 1: Find the set of prime numbers less than 30:
To solve this, you need to identify all the prime numbers that are less than 30. A prime number is a number that is divisible only by 1 and itself without leaving a remainder. Start by listing the prime numbers less than 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Step 2: Find the set of odd numbers greater than zero:
Now we need to identify the odd numbers greater than zero. Odd numbers are the ones that cannot be divided evenly by 2. In this case, all positive odd numbers are the elements we are looking for.
Step 3: Find the intersection:
To find the intersection, we need to identify the numbers that appear in both sets. In this case, we need to find the prime numbers less than 30 that are also odd. Looking at our list of prime numbers, we see that the odd prime numbers less than 30 are: 3, 5, 7, 11, 13, 17, 19, 23, and 29.
Step 4: Count the numbers in the intersection:
Counting these numbers, we can see that there are 9 elements in the intersection of the two sets.
So, the answer to the question "How many elements are in the intersection of the set of all the prime numbers less than 30 and the set of all the odd numbers greater than zero?" is 9.
Remember, understanding the concepts behind solving a problem is just as important as finding the answer. So, practice with similar questions to solidify your understanding.