Final answer:
To find (A∪B)∪C, we first find the union A∪B, which is {4, 5, 6, 7, 8, 9, 10, 12, 14}, and then we unite this with set C to get {1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}, including all unique elements from sets A, B, and C.
Step-by-step explanation:
To find (A∪B)∪C using the given sets, first we need to determine the elements of set A∪B, which represents the union of A and B. This union includes all the elements that are either in set A or in set B or in both, without repeating any elements. Then we combine this union with set C to find the ultimate union.
The given sets are:
- A = {4,5,6,7,8,9}
- B = {4,6,8,10,12,14}
- C = {1,3,5,7,9,11,13,15}
To find A∪B, we combine the unique elements:
A∪B = {4, 5, 6, 7, 8, 9, 10, 12, 14}
Then we take this union and combine it with set C to get (A∪B)∪C:
(A∪B)∪C = {1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
Note that we include each element only once even if it appears in more than one set.