Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10}; B = {2, 3, 5, 7}. Write the set (A U B)’.
Question
Let
U = {x : x ∈ N, x ≤ 9};
A = {x : x is an even number, 0 < x < 10};
B = {2, 3, 5, 7}.
Write the set (A U B)’.
Solution
To find the set (A U B)', we need to first find the union of sets A and B.
Set A consists of even numbers between 0 and 10, excluding 0 and 10. So, A = {2, 4, 6, 8}.
Set B consists of the prime numbers 2, 3, 5, and 7. So, B = {2, 3, 5, 7}.
The union of sets A and B, denoted as A U B, is the set that contains all the elements from both sets A and B. So, A U B = {2, 3, 4, 5, 6, 7, 8}.
Now, to find the complement of the set A U B, denoted as (A U B)', we need to find all the elements that are not in the set A U B but are in the universal set U.
The universal set U is defined as the set of natural numbers less than or equal to 9. So, U = {1, 2, 3, 4, 5, 6, 7, 8, 9}.
To find (A U B)', we need to find the elements in U that are not in A U B.
(A U B)' = {1, 9}.
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