For S = the set of whole numbers
A = the set of numbers which are perfect squares
B = the set of positive even numbers
describe:
a.) A'
b.) AUB
c.) (AUB)'
What exactly is the question
Assuming the universal set, E is the set of whole numbers, thus
E=S={...-2000, -1999, ...-2,-1,0,1,2,3,...1926, 1927...}
A={1,4,9,16,25,...}
B={2,4,6,8,...}
A'=complement, i.e. a set containing all members except A, therefore
A'=any whole number that is not a perfect square,
∪=union, combine two sets together.
A∪B=whole numbers that are either a perfect square or even
Can you figure out what is (A∪B)'?
To describe the given sets, we'll break down each expression step-by-step:
a.) A'
The set A' represents the complement of A. The complement of a set consists of all the elements that are not in the original set.
In this case, A represents the set of numbers which are perfect squares. So, A' would be the set of numbers that are not perfect squares.
To find A', you can consider taking the set of whole numbers (S) and removing all the elements that are perfect squares. This would result in A' representing all the whole numbers that are not perfect squares.
b.) AUB
The expression AUB represents the union of sets A and B. The union of two sets consists of all the elements that are present in either of the two sets.
In this case, A represents the set of numbers which are perfect squares, and B represents the set of positive even numbers. AUB would be the set that contains all the numbers that are either perfect squares or positive even numbers or both.
For example, A = {0, 1, 4, 9, 16} and B = {2, 4, 6, 8}. Their union AUB would be {0, 1, 2, 4, 6, 8, 9, 16}.
c.) (AUB)'
The expression (AUB)' represents the complement of the union of sets A and B. It consists of all the elements that are not present in the union of A and B.
To find (AUB)', we first need to find the union of sets A and B (AUB) as described in the previous step. Then, we take the whole numbers set (S) and remove all the elements that are present in the union (AUB). This would result in (AUB)' representing all the whole numbers that are not in the union of sets A and B.