Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P = {1, 2, 3, 4}. What is P'?
A.{5, 6, 7, 8}***
B.{1, 2, 3, 4, 5, 6, 7, 8}
C.{1, 2, 3, 4}
D.cannot be determined
To find P', we need to find the complement of set P within the universal set U.
1. Start with the universal set U = {1, 2, 3, 4, 5, 6, 7, 8}.
2. Take set P = {1, 2, 3, 4}.
3. Remove all elements of P from U.
- U - P = {5, 6, 7, 8}.
4. The resulting set {5, 6, 7, 8} is the complement of set P within the universal set U.
5. Therefore, P' = {5, 6, 7, 8}.
So, the correct answer is A. {5, 6, 7, 8}.
To find the complement of set P, denoted as P', you need to find all the elements in the universal set that are not in P.
First, let's determine the elements in P. According to the given information, P = {1, 2, 3, 4}.
Now, let's find the complement of P. This means we need to find all the elements in the universal set that are not in P.
The universal set U = {1, 2, 3, 4, 5, 6, 7, 8}.
To find P', we need to subtract the elements in P from the elements in the universal set, U.
U - P = {5, 6, 7, 8}
Therefore, P' = {5, 6, 7, 8}.
So, the correct answer is option A. {5, 6, 7, 8}.