U is the set of positive integers less than or equal to 30. A is the set of natural numbers that are multiples of 5 in U. B is the subset of all of the even integers in U.
a) Find n(A U B)
b) Find n(A intersect B)
c) Find n(A U B' )
d Find n(B intersect A')
Thank you so much!!!!!
So, can you decide the contents of A and B?
To solve these questions, we need to understand the concepts of sets and set operations. Let's break down each question step by step.
a) Find n(A U B):
The symbol U represents the union of sets A and B, which means we need to combine all the elements from set A and set B. In this case, A represents the natural numbers that are multiples of 5 in set U, and B represents the subset of even integers in set U.
To find n(A U B), we simply need to count the number of elements in the combined set A U B.
First, let's find the elements of set A:
A = {5, 10, 15, 20, 25, 30}
Next, let's find the elements of set B:
B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}
Now, combine both sets A and B without including any duplicates:
A U B = {2, 4, 5, 6, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 25, 26, 28, 30}
Finally, count the number of elements in the set A U B, which is n(A U B).
b) Find n(A intersect B):
The symbol intersect (∩) represents the intersection of sets A and B. The intersection of two sets is the set of elements that are common to both sets.
To find n(A intersect B), we need to find the elements that are present in both set A and set B.
Set A = {5, 10, 15, 20, 25, 30}
Set B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}
The elements present in both set A and set B are:
A ∩ B = {10, 20, 30}
Finally, count the number of elements in the set A ∩ B, which is n(A ∩ B).
c) Find n(A U B'):
The symbol ' represents the complement of a set. The complement of set B (B') contains all the elements from the universal set U that are not present in set B.
To find n(A U B'), we need to find the elements in set A that are also not present in set B.
Set A = {5, 10, 15, 20, 25, 30}
Set B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}
The elements in set A that are not present in set B are:
A U B' = {5, 15, 25}
Finally, count the number of elements in the set A U B', which is n(A U B').
d) Find n(B intersect A'):
To find n(B intersect A'), we need to find the elements that are present in set B and are not present in set A.
Set A = {5, 10, 15, 20, 25, 30}
Set B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}
The elements in set B that are not present in set A are:
B ∩ A' = {2, 4, 6, 8, 12, 14, 16, 18, 22, 24, 26, 28}
Finally, count the number of elements in the set B ∩ A', which is n(B ∩ A').
Make sure to substitute the actual numbers when calculating each value to get the precise answers.