answer:To find the complement of set A, we need to define a universal set U that contains all possible elements, including those in set A. The complement of set A, denoted as A', consists of all elements in U that are not in set A. Let's assume the universal set U contains the integers from 1 to 10, i.e., U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Now we can find the complement of set A. A' = {x ∈ U | x ∉ A} A' = {7, 8, 9, 10} To show that the complement of set A is unique, we need to prove that there is no other set B' that can be the complement of set A. Suppose there is another set B' that is the complement of set A. Then, B' must also satisfy the condition that all elements in B' are not in set A. Since A' and B' both contain elements not in set A, and there are no other elements in the universal set U that are not in set A, A' and B' must contain the same elements. Therefore, A' = B', and the complement of set A is unique.

answer:To find the complement of set A, we first need to define the universal set U, which contains all the elements under consideration. The complement of A, denoted as A', will contain all the elements in U that are not in A. Let's assume that the universal set U contains all the integers from 1 to 10. Then, U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Now, we can find the complement of A. A' = {x ∈ U | x ∉ A} Comparing the elements of U and A, we can see that the elements 1, 3, 5, 7, 9, and 10 are not in A. Therefore, the complement of A is: A' = {1, 3, 5, 7, 9, 10} Now, let's prove that this complement set is unique. Suppose there exists another set B such that B is also the complement of A. Then, by definition, B must also contain all the elements in U that are not in A. Since A and B are both complements of A, they must have the same elements. Therefore, B must also contain the elements 1, 3, 5, 7, 9, and 10. Since A' and B have the same elements, they are equal: A' = B Thus, the complement of A is unique, and it is the set A' = {1, 3, 5, 7, 9, 10}.

answer:The complement of a set B with respect to a universal set A, denoted as B', is the set of all elements in A that are not in B. Given the universal set A = {1, 2, 3, 4, 5, 6} and set B = {2, 4, 6}, we can find the complement of set B as follows: B' = {x ∈ A | x ∉ B} Comparing the elements of set A and set B, we can see that the elements 1, 3, and 5 are not in set B. Therefore, the complement of set B is: B' = {1, 3, 5} To verify that the complement of set B is unique, we need to show that there is no other set that can be the complement of set B with respect to set A. Since set A is the universal set, any other subset of A that is not equal to B' would either contain elements from set B or not contain some elements from B'. In either case, it would not be a complement of set B. Thus, the complement of set B is unique, and it is B' = {1, 3, 5}.

answer:To determine the size of B and C, we need to know the size of the universal set, which contains all elements under consideration. The complement of a set A, denoted by A', B, or C in this case, contains all elements in the universal set that are not in A. Without knowing the size of the universal set, we cannot determine the size of B and C.