Given that P is the set of all prime numbers between 0 and 10, and Q is the set of all odd numbers between 0 and 10. Find the union of elements in P that ar...

Answer Details

To solve this problem, we will first identify the elements in both sets P and Q:

The set P, which consists of all the prime numbers between 0 and 10, is {2, 3, 5, 7}. A prime number is a number greater than 1 that has no divisors other than 1 and itself.

The set Q, which consists of all odd numbers between 0 and 10, is {1, 3, 5, 7, 9}. An odd number is any integer that is not divisible by 2.

The problem requires us to find:

• Elements in P that are not in Q
• Elements in Q that are not in P

Now, let's find these two sets:

1. Elements in P that are not in Q: Look at set P and remove any elements that are also in set Q.

• From P: {2, 3, 5, 7}
• From Q: We remove 3, 5, and 7 (as they are present in both sets)
• So, the remaining element in P that are not in Q is {2}

2. Elements in Q that are not in P: Look at set Q and remove any elements that are also in set P.

• From Q: {1, 3, 5, 7, 9}
• From P: We remove 3, 5, and 7 (as they are present in both sets)
• So, the remaining elements in Q that are not in P are {1, 9}

Finally, let's find the union of the elements: Combine the results from both parts.

• Elements from P that are not in Q: {2}
• Elements from Q that are not in P: {1, 9}
• The union of these two sets is {1, 2, 9}

Therefore, the answer is {1, 2, 9}.