Suppose U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set and Q = {3, 6, 9}. What is Q'?
Q' is denoted as the complement of set Q in the universal set U. It consists of all the elements in U that are not in Q.
The elements in Q' can be calculated as follows:
Q' = U - Q
Q' = {1, 2, 4, 5, 7, 8, 10}
To find Q', which is the complement of set Q, we need to determine the elements in U that are not in Q.
Step 1: Start with the universal set, U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Step 2: Identify the elements in Q, which are 3, 6, and 9.
Step 3: Remove these elements from U to find Q'.
Q' = {1, 2, 4, 5, 7, 8, 10}
Therefore, the complement of set Q is Q' = {1, 2, 4, 5, 7, 8, 10}.
To find Q', also known as the complement of set Q, you need to find all the elements that are in the universal set U but not in set Q.
Here's how you can find Q':
1. Start by listing all the elements in the universal set U: U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
2. Now, identify the elements in set Q: Q = {3, 6, 9}.
3. To find the complement Q', exclude all the elements in set Q from the universal set U.
- Remove 3 from U: U - 3 = {1, 2, 4, 5, 6, 7, 8, 9, 10}.
- Remove 6 from U': U - 3 - 6 = {1, 2, 4, 5, 7, 8, 9, 10}.
- Remove 9 from U': U - 3 - 6 - 9 = {1, 2, 4, 5, 7, 8, 10}.
4. The resulting set is the complement of Q, written as Q' = {1, 2, 4, 5, 7, 8, 10}.
Therefore, Q' is the set {1, 2, 4, 5, 7, 8, 10}.