Final answer:
To find the common elements in set U (whole numbers greater than 85 but smaller than 100), set M (odd numbers), and set N (prime numbers), list numbers 86-99, identify the odd numbers, and then determine which of these are prime. The resulting intersection is {89, 97}.
Step-by-step explanation:
The question involves finding the common elements between three sets: U, the set of whole numbers greater than 85 but smaller than 100; M, the set of odd numbers; and N, the set of prime numbers. To solve this, we identify the numbers 86 through 99 that are both odd and prime. These are the numbers that would be included in the intersection of sets U, M, and N.
First, list the whole numbers from 86 to 99, which are in set U:
- 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99
Next, from this list, we identify the odd numbers, which are also the numbers in set M:
- 87, 89, 91, 93, 95, 97, 99
Finally, we find the prime numbers from the list of odd numbers, as prime numbers are elements of set N:
Therefore, the intersection of sets U, M, and N (U ∩ M ∩ N) is the set {89, 97}.
The complete question is: U=(whole numbers greater than 85 but smaller than 100) M = (odd numbers ) N = (prime numbers) is: