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4 cards from this section. Quick, good the night before a test.
Provide an example of a symmetric relation.
Think of relationships where mutual conditions apply.
Define a reflexive relation.
What condition must always hold true in a reflexive relation?
What defines a symmetric relation?
Think about relations that require mutual connections.
True or False: An anti-symmetric relation can have (a, b) and (b, a) both present if a does not equal b.
Remember the definition of anti-symmetry.
Construct a relation on 4 elements that is symmetric yet not reflexive. Describe your relation.
What must you include while maintaining symmetry and excluding reflexivity?
Prove that any reflexive relation on a set is not anti-symmetric if it includes all pairs.
Look closely at the definitions and what full inclusion means.
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