April 2024
Intermediate to advanced
327 pages
11h 16m
English
(1.1) The relation is an equivalence relation:
Reflexivity: x attends the same class as x.
Symmetry: If x attends the same class as y, then y also attends the same class as x.
Transitivity: If x attends the same class as y and y attends the same class as z, then x and z also attend the same class.
(1.2) The relation is not transitive and hence not an equivalence relation, as seen in this family tree:

Alice and Bob share a grandparent (Joel), and Bob and Carol share a grandparent (Kathie), but Alice and Carol do not.
(1.3) The relation x ∼ y ⇔ xTy = 0 is not reflexive for x ≠ 0 and hence ...
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