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3 cards from this section. Quick, good the night before a test.
What is a partition of a set?
Think about how subsets can combine back to the original set.
Define an equivalence relation.
Consider the properties of relationships.
What is a characteristic of a partition?
Remember the requirements for a partition.
True or False: An equivalence relation requires that all elements relate to each other.
Consider how equivalence classes function.
Given a set A = {1, 2, 3, 4, 5}, create all possible partitions and identify their equivalence classes.
Start by generating smaller partitions and build from there.
Prove that if you have a partition of a set, you can produce an equivalence relation whose equivalence classes are those subsets.
Use examples from known partitions to visualize your explanation.
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