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2 cards from this section. Quick, good the night before a test.
Define a reflexive relation on the set {a, b}.
Remember that every element must relate to itself.
What is an example of an irreflexive relation on the set {x, y}?
Ensure none of the pairs (x, x) or (y, y) are included.
What defines a reflexive relation?
Think about how elements relate to themselves.
True or False: An empty set can be both reflexive and irreflexive.
Consider how there are no elements to contradict the definitions.
Given set A = {1, 2, 3}, define a reflexive relation, then modify it to make it irreflexive without removing elements.
Reflexivity requires self-relations, irreflexivity denies them.
Is it possible to have a single relation that is both reflexive and irreflexive? Explain your reasoning.
Consider what happens when you have no items at all.
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