Question

Given the following sets of numbers, what

is the complement of set A?
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {3, 5, 7, 10)
A' = {[ ? ]}
A. 3, 5, 7, 10
B. 1, 2, 4, 6, 8, 9
C. 5, 6, 7, 8, 9, 10
D. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Answer 1

The complement of set A, denoted as A', is the set of elements in the universal set U that are not in A. For U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {3, 5, 7, 10}, the complement is A' = {1, 2, 4, 6, 8, 9}. The correct answer is option B.

Step-by-step explanation:

The complement of a set A, denoted as A', includes all the elements that are in the universal set U but not in set A. For the given sets, U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {3, 5, 7, 10}, the complement of A, A', would be all the numbers from the universal set U that are not in A. To find A', we simply list all the elements from U that are not found in A. Therefore, A' = {1, 2, 4, 6, 8, 9}. Since 3, 5, 7, and 10 are in set A, they are excluded from the complement. Comparing our found set for A' with the provided options, the correct answer is B. 1, 2, 4, 6, 8, 9, which represents all the elements not in set A within the universal set U.