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3 cards from this section. Quick, good the night before a test.
Define what a partition is in your own words.
Think about how subsets relate to the whole set.
List the three conditions for a valid partition.
Recall the definitions we discussed.
What must be true for subsets in a partition of a set?
Recall the definition of partitioning.
True or False: The equivalence classes formed from an equivalence relation can overlap.
Think about what it means for classes to be equivalent.
Given the set S = {a, b, c, d, e} and the partition {{a, b}, {c, d}, {e}}, construct an equivalence relation and justify why it meets the criteria for reflexivity, symmetry, and transitivity.
Focus first on proving one property of equivalence at a time.
In a university, students are classified into departments: {Math, Science}, {Arts}, and {Engineering}. Create a practical example showing a partition into departments and derive its corresponding equivalence relation.
Think about how you can link students to different departments for clarification.
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