Equivalence Relations
An equivalence relation R must have three properties
- reflexive: for any x, xRx is true
- symmetric: for any x and y, xRy implies yRx
- transitive: for any x, y, and z, xRy and yRz implies xRz
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Connection between rooms is an equivalence relation
- any room is connected to itself
- if room a is connected to room b, then room b is connected to room a
- if room a is connected to room b and room b is connected to room c, then room a is connected to room c