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In this preview activity, we will explore some basic properties of sets and functions. Later in this section, we will write proofs about these ideas.
1.
Remember that a set is just a collection of elements. Here are two definitions about sets:
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Given sets
and the union of and written is the set containing every element that is in or or both.
Letβs build some examples.
(a)
(b)
(c)
2.
3.
For any function and any set we can define the image of under to be the set of all outputs of when the input is an element of We write this as