Let U= {1,2,3, . . .},
A= {1, 2, 3, . . . ., 39}.
use the roster method to write the set A'
Find A' =
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I understand how complements work. Complement A' is everything outside of set A. However, since U goes on infinitely with its ellipsis, how do I know exactly what the complement of A' is?
Help, please?
simple: A' = {40,41, ...}
To find the complement of set A', we need to determine all the elements in the universal set U that are not in set A.
Given that U = {1, 2, 3, ...}, and A = {1, 2, 3, ..., 39}, we can write the set A' using the roster method as follows:
A' = {x ∈ U | x ∉ A}
To find the complement, we need to include all elements in the universal set U that are not in set A. However, since the universal set U goes on infinitely, we cannot list all the elements individually.
In this case, since set A contains all the positive integers up to 39, the complement A' would include all the positive integers greater than 39 that are in the universal set U. But, since U is infinite, it is not possible to provide an exhaustive list of all the elements in the complement.
So, in this case, the set A' can be expressed as:
A' = U \ A
Where "U \ A" denotes the set difference, representing all elements in U that are not in A.
To find the complement of set A, denoted as A', we need to consider the universal set U and exclude all the elements that belong to A. In this case, U includes all the natural numbers starting from 1.
Since A consists of all the natural numbers from 1 to 39, we need to find the set of numbers that are not in A, i.e., the complement of A in U.
To write A' in roster method, we can list all the elements that are not in A. In this case, the elements not in set A are:
40, 41, 42, 43, ...
As you mentioned, the universal set U has an ellipsis indicating an infinite number of elements. Therefore, we represent the complement of A' as all the natural numbers greater than 39.
Hence, using the roster method, A' can be written as:
A' = {40, 41, 42, 43, ...}