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2 cards from this section. Quick, good the night before a test.
Define an equivalence relation.
Think about the three properties that must be satisfied.
What does it mean to partition a set?
Consider how groups of elements can be formed.
What defines an equivalence relation?
Remember the properties we discussed using RST.
Does every partition of a set form an equivalence relation?
Think about how each element is categorized.
Given a set with 50 elements, partition this set into four equal subsets and find the number of ordered pairs within each subset.
Break down the problem by first finding the size of each subset.
Prove that if a relation R on a set A is reflexive and symmetric, it does not imply R is transitive. Provide a counterexample.
Reflect on how pairing can lead to violations of transitivity.
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