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2 cards from this section. Quick, good the night before a test.
What is meant by the term transitive closure?
Think about connectivity and closure in conditions.
Define a connectivity relation.
Consider what paths would mean in a graph context.
What is the connectivity relation R*?
Think about how paths function within graph representations.
If (a, b) is in R* and (b, c) is also in R*, what can we conclude?
R* should maintain transitive characteristics.
Create a boolean matrix for a given relation R with 5 elements and calculate R*.
Use boolean multiplication and ensure to check reachable paths.
Prove that R* is the smallest transitive relation expanding R using set theory.
Visualize subsets and demonstrate transitivity through multiple examples.
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