1.
Remember that a set is just a collection of elements. Here are two definitions about sets:
- A set \(A\) is a subset of a set \(B\text{,}\) written \(A \subseteq B\) provided every element in \(A\) is also an element of \(B\text{.}\)
- Given sets \(A\) and \(B\text{,}\) the union of \(A\) and \(B\text{,}\) written \(A \cup B\) is the set containing every element that is in \(A\) or \(B\) or both.
Let’s build some examples.
(a)
Let \(B = \{1, 3, 5, 7, 9\}\text{.}\) Give an example of a set \(A\) containing \(3\) elements that is a subset of \(B\text{.}\)
What is \(A \cup B\) for the set \(A\) you gave as an example?
(b)
Give an example of two sets distinct sets \(A\) and \(B\) such that \(A \cup B = B\text{.}\)
\(A =\) ; \(B =\)
For the example you gave, is \(A \subseteq B\text{?}\)
- yes
- no
(c)
Find examples, if they exist, of sets \(A\) and \(B\) such that \(A \cup B \ne B\text{.}\)
\(A =\) ; \(B =\) .
For the example you gave, is \(A \subseteq B\text{?}\)
- yes
- no